Computer Aided Design (CAD)

The previous sections dealt with the initial and middle stages of reverse engineering. This section highlights a stage which is undoubtedly crucial for product development. After a meshed part is aligned, it goes through either—surface modeling in tools such as Polyworks, which generates a non-parametric model (IGES or STEP format) or parametric modeling where a sketch of the meshed part is created instead of putting it through surfacing (.PRT format). The resultant is generally called, 3D computer aided model or CAD model.

But, what is CAD?  

CAD is the acronym for Computer Aided Design. It covers different variety of design tools used by various professionals like artists, game designers, manufacturers and design engineers.

The technology of CAD systems has tremendously helped users by performing thousands of complex geometrical calculations in the background without anyone having to drop a sweat for it. CAD has its origin in early 2D drawings where one could draw objects using basic views: top, bottom, left, right, front, back, and the angled isometric view.  3D CAD programs allow users to take 2D views and convert them into a 3D object on the screen.  In simple definition, CAD design is converting basic design data into a more perceptible and more understandable design.

Each CAD system has its own algorithm for describing geometry, both mathematically and structurally.  

Different CAD models

Everything comes with its own varieties and CAD modeling is no stranger to it. As the technology evolved, CAD modeling came up in different styles. There are many methods of classifying them, but a broad general classification can be as follows:

  • 2 dimensional or 2D CAD: The early version of CAD that most of us are aware of. These are 2-dimensional drawings on flat sheet with dimensions, layouts and other information needed to manufacture the object.
  • 3 dimensional or 3D CAD: The purpose of both 2D and 3D models is the same. But what sets 3D models apart is its ability to present greater details about the individual component and/or assembly by projecting it as a full-scale 3-dimensional object. 3D models can be viewed and rotated in X, Y, or Z axes. It also shows how two objects can fit and operate which is not possible with 2D CAD.

3D models can be further classified into three categories:

  • 3D Wire-frame Models: These models resemble an entire object made of just wires, with the background visible through the skeletal structure.
  • Surface Models: Surface models are created by joining the 3D surfaces together and look like real-life objects.
  • Solid Models: They are the best representation of real physical objects in a virtual environment. Unlike other models, solid models have properties like weight, volume and density. They are the most commonly used models and serve as prototypes for engineering projects.

CAD model

Types of CAD formats

Different professionals use different software, owing to different reasons like cost, project requirements, features etc. Although, software comes with their own file formats, there are instances where one needs to share their project with someone else, either partners or clients, who are using different software. In such cases, it is necessary that both party software understand each other’s file formats. As a result of this situation, it is necessary to have file formats which can be accommodated in variety of software.

 CAD file formats can be broadly classified into two types:

  • Native File Formats: Such CAD file formats are intended to be used only with the software it comes with. They cannot be shared with any other software which comes with their own CAD formats.
  • Neutral File Formats: These file formats are created to be shared among different software. Thereby it increases interoperability, which is necessary.

 Although there are almost hundreds of file formats out there, the more popular CAD formats are as follows:

STEP: This is the most popular CAD file format of all. It is widely used and highly recommended as most software support STEP files. STEP is the acronym for Standard for the Exchange of Product Data.

IGES: IGES is the acronym for Initial Graphics Exchange Specification. It is an old CAD file format which is vendor-neutral. IGES has fallen out lately since it lacks many features which newer file formats have.

Parasolid: Parasolid was originally developed by ShapeData and is currently owned by Siemens PLM Software.

STL: STL stands for Stereolithography which is the format for 3D information created by 3D systems. STL finds its usage mostly in 3D printers. STL describes only the outer structure or surface geometry of a physical object but doesn’t give out color, texture and other attributes of an object.

VRML: VRML stands for Virtual Reality Modeling Language. Although it gives back more attributes than STL but it can be read by a handful of software.

X3D: X3D is an XML based file format for representing 3D computer graphics.

COLLADA: COLLADA stands for Collaborative Design Activity and is mostly used in gaming and 3D modeling.

DXF: DXF stands for Drawing Exchange Format which is a pure 2D file format native to Autocad.

Use of CAD

Computer-aided design or CAD has pushed the entire engineering process to the next level. One can actually mould or fold, modify or make a new part from scratch, all with the help of CAD modeling software. The many uses of CAD are as follows:

  • CAD is used to generate design and layouts, design details and calculations, 3-D models.
  • CAD transfers details of information about a product in a format that can be easily interpreted by a skilled professional, which therefore facilitates manufacturing process.
  • The editing process in CAD is very fast as compared to manual process.
  • CAD helps in speeding up manufacturing process by facilitating accurate simulation, hence reducing time taken to design.
  • CAD can be assimilated with CAM (Computer Aided Manufacturing), which eases up product development.
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DFMA and DFMEA

During the last few decades, with the developments in technology, manufacturers have been enabled to source parts globally. More and more manufacturers have entered the competition as it grows fierce. Companies in developing nation market offer products at lower prices. To sustain business and achieve growth, many manufacturers are coming up with new products to cater to the consumers and widen it as well. They must be very marketable and of high quality. The Design for Manufacturing and Assembly (DFMA) method enables firms to develop quality products in lesser time and at lower production costs.

Design for Manufacturing and Assembly (DFMA)

Design for Manufacturing and Assembly or DFMA is a design process that targets on ease of manufacturing and efficiency of assembly.

Simplifying the design of a product makes it possible to manufacture and assemble it in the minimum time and lower cost. DFMA approach has been used in the automotive and industrial sectors mostly. However, the process has been adopted in the construction domain as well.

DFMA is a combination of two methodologies which are:

  • Design for Manufacturing (DFM): DFM focuses on the design of constituent parts to ease up their manufacturing process. The primary goal is to select the most cost-efficient materials and procedures to be used in production and minimize the complexity of the manufacturing operations.
  • Design for Assembly (DFA): DFA focuses on design for the ease of assembly in the product. The aim is to reduce product assembly cost and minimize the number of assembly operations.

Both DFM and DFA seek to reduce material, labour costs associated with designing and manufacture of a product. For a successful application of DFMA, the two activities should operate in unison to earn the most significant benefit. Through the DFMA approach, a company can prevent, detect, quantify, and eliminate waste and manufacturing inefficiency within a product design.

Design Failure Mode and Effect Analysis (DFMEA)

Design Failure Mode and Effect Analysis (DFMEA) is a methodical string of activities to identify and analyze potential systems, products, or process failures.

Design Failure Mode and Effects Analysis or DFMEA focuses on finding potential design flaws and failures of components before they can make a significant impact on the end users of a product and the business distributing the product.

DFMEA identifies –

The potential risks introduced in a  new or modified design,

 The effects and outcomes of failures,

The actions that could eliminate the failures, and

provides a historical written record of the work performed. 

DFMEA is an ideal process for any sector where risk reduction and failure prevention are crucial, which includes:

  • Manufacturing
  • Industrial
  • Aerospace
  • Software
  • Service industries

 

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Difference between New Product Development (NPD) & Industrial Design (ID)

Let us take a step back and walkthrough the definitions as presented earlier in this article.

New Product Development: The process which involves forming strategy, organizing requirements, generating concepts, creating product & marketing plan, evaluating and subsequent commercialization, thereby bringing a new product to the marketplace.

Product development is a complete cycle which starts from market analysis, product specifications to concept/industrial design, costing, scheduling, testing, manufacturing and ends at logistics, customer feedback, improvements and the final act of getting a product into the market.

Industrial Design:The practice of forming concepts and designing products, which are to be manufactured through techniques of mass production.

Product Design is complete process that includes product industrial design, user experience, 3D Cad modeling, design calculations, simulation. Responsibility of a good product design is to make product working as per design specifications. It is safe to say that product industrial design is one of the many stages of NPD. It is a crucial subset of NPD which is necessary for the successful completion of entire development cycle.

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FEA, CFD and Mold Flow Analysis

Over the years, the term “Design Analysis” has found a significant place for itself in the manufacturing sector. Instead of making a prototype and creating elaborate testing regimens to analyze the physical behavior of a product, engineers can evoke this information quickly and accurately on the computer.

Design analysis is a specialized computer software technology designed to simulate the physical behavior of an object.

If an object will break or deform or how it may react to heat are the sort of queries design analysis can answer. Design analysis helps in minimizing or even eliminate the need to build a physical prototype for testing. As a result, the technology has gone mainstream as a prized product development tool and found its presence in almost all sectors of engineering.

This article discusses three major design analysis software, namely:

  • Finite Element Analysis (FEA)
  • Computational Fluid Dynamics (CFD)
  • Mold Flow Analysis
Finite Element Analysis (FEA)

The Finite Element Analysis (FEA) is a specialized simulation of a physical entity using the numerical algorithm known as Finite Element Method (FEM). It is used to reduce the number of physical prototypes and experiments and analyze objects in their design stage to develop better products faster. The term ‘finite’ is used to denote the limited, or finite, number of degrees of freedom used to model the behavior of each element.

FEA will analyze an object in question by breaking down its entire geometry into small ‘elements,’ which are put under simulated conditions see how the elements react. It displays the results as color-coded 3D images where red denotes an area of failure, and blue indicates fields that maintain their integrity under the load applied. However, note it down that FEA gives an approximate solution to the problem.

Mathematics is used to understand and quantify a physical phenomena such as structural or fluid behavior, wave propagation, thermal transport, the growth of biological cells, etc. Most of these processes are described using Partial Differential Equations. Finite Element Analysis has proven to be on of the most prominent numerical technique for a computer to solve these PEDs.

FEA is used in:

Problems where analytical solution is not easily obtained,

And mathematical expressions required because of complex geometries, loadings and material properties.

Computational Fluid Dynamics (CFD)

Computational Fluid Dynamics (CFD) is a specilaized simulation used for the analysis of fluid flows through an object using numerical solution methods. CFD incorporates applied mathematics, physics and computing software to evaluate how a gas or liquid flows and how it affects an object as it flows past. CFD is based on Navier-Stokes equations which describe the way velocity, temperature, pressure, and density of a moving fluid are related.

Aerodynamics and hydrodynamics are two engineering streams where CFD analyses are often used. Physical quantities such as lift and drag or field properties as pressures and velocities are computed using CFD. Fluid dynamics is connected with physical laws in the form of partial differential equations. Engineers transform these laws into algebraical equations and can efficiently solve these equations numerically.The CFD analysis reliability depends on the whole structure of the process. The determination of proper numerical methods to develop a pathway through the solution is highly important. The software, which conducts the analysis is one of the key elements in generating a sustainable product development process, as the amount of physical prototypes can be reduced drastically.

CFD is used in almost all industrial domains, such as:

  • Food processing
  • Water treatment
  • Marine engineering
  • Automotive
  • Aerodynamics
  • Aerospace

With the help of CFD, fluid flow can be analyzed faster in more detail at an earlier stage, than by tesing, at a lower cost and lower risk. CFD solves the fundamental equations governing fluid flow processes, and provides information on important flow characteristics such as pressure loss, flow distribution, and mixing rates.

CFD has become an integral part of engineering and design domains of prominent companies due to its ability to predict performance of new designs and it intends to remain so.

Mold Flow Analysis

Moldflow, formerly known as C-mould, is one of the leading software used in processwide plastics solutions. Mold flow computes the injection molding process where plastic flows into a mold and analyzes the given mold design to check how the parts react to injection and ensure that the mold will be able to produce the strongest and uniform pieces. Two of the most popular mold flow analysis software are Moldflow and Moldex3D used exclusively by many mold makers.

There are three types of Mold flow analysis which are as follows:

  • Moldflow Filling Analysis (MFA): It facilitates visualization of shear rate and shear stress plus determination of fiber orientation and venting. MFA can predict fill pattern and injection pressure while optimizing gating and runner system.
  • Moldflow Cooling Analysis (MCA): MCA specializes in finding hot spots and calculating time to freeze. It helps in determining uneven cooling between core and cavity while specifying required cooling flow rates.
  • Moldflow Warpage Analysis (MWA): Moldflow warpage is all about predicting, finding and determining warpage due to orientation.

We can see benefits of using different analysis procedures that correctly understand the power of the different simulation tools. During the product design, many these methods affect the cost and quality of the product, thereby ensuring the optimum productivity as aimed by the manufacturer.

 

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Geometric Dimensioning and Tolerancing (GD&T)

The design model is a depiction of a part design. However, the design model can never be an accurate representation of the product itself. Due to shortcomings in manufacturing and inspection processes, physical parts never match the design model exactly. An essential aspect of a design is to specify the lengths the part features may deviate from their theoretically accurate geometry. It is vital that the design intent and functionality of the part be communicated between the design engineers and the manufacturing unit. It is where the approach of GD&T comes into play.

Geometric dimensioning and tolerancing or GD&T is a language of symbols and standards used on engineering drawings and models to determine the allowable deviation of feature geometry. 

GD&T consists of dimensions, tolerances, definitions, symbols, and rules that enable the design engineers to convey the design models appropriately. The manufacturing unit uses the language to understand the design intent.

To master GD&T, one needs to understand the crucial concepts, which includes:

  • Machining tolerances: Tolerances mean the allowable amount of deviation from the proposed drawing. Machined parts look flat and straight through the naked eye, but if viewed with calipers, one can find imperfections all over. These imperfections or variations are allowed within the tolerance constraints placed on the parts. Tolerances should be kept as large while preserving the functions of the part.
  • The Datum Reference Frame: DRF is the most important aspect of GD&T. It is a three-dimensional cartesian coordinate system. It’s a skeletal reference to which all referenced geometric specifications are related.
  • GD&T Symbols: It is essential to be familiar with numerous symbols and types of applied tolerance in GD&T. The language of symbols makes it easier to interpret designs and improve communications from the designer to the shop. By using GD&T standard, the design intent is fully understood by suppliers all over the world.

  • Feature Control Frame: The feature control frame describes the requirements or instructions for the feature to which it is attached. A feature control frame contains only one message. If a feature needs two messages, the feature would need the corresponding amount of feature control frames for every message required.
  • Basic Dimensions: Basic dimensions are exact numerical values in theory, which defines the size, orientation, form, or location of a part or feature. 
  • Material Condition Modifiers: It is often necessary to state that a tolerance applies to a feature at a particular feature size. The Maximum Material Condition (MMC) allows an engineer to communicate that intent.

GD&T is an efficient way to describe the dimensions and tolerances compared to traditional approximation tolerancing. The engineer might design a part with perfect geometry in CAD, but the produced part, more often than not, turns out to be not accurate. Proper use of GD&T improves quality and reduce time and cost of delivery by providing a common language for expressing design intent.

 

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Importance of Product Development(NPD) & Industrial Design(ID) for a business

Over the first fiscal quarter of 2018, Apple accelerated investments in research and development operations spending more than $3.4 billion on new hires and initiatives which will keep the company competitive in a fast-paced tech market.

Product development is like the gasoline that keeps the wheels rolling. But what drives companies to spend valuable resources such as time, money, human capital, etc. on new product development? And why is it so important?

 Here are five reasons:

  • Value for customers

The primary reason for any new product development is to provide value to its customers. The increasing demands of customers for innovation & new technology calls for the need to develop new or existing products. Otherwise, there is no reason to pour in huge amounts of money in the first place.

  • Keeping up with the competition

Staying ahead of the competition should always be the primary goal for any business. And increased competition is one of the major reasons leading to go for new products development. New products give us a competitive advantage over our rivals. Every firm struggles to fulfill and retain consumers by offering exceptional products. To offer more competitive advantage over the other and to satisfy consumer needs more effectively and efficiently, the product innovation seems to be needed.

  • Changing markets

Today’s market is more dynamic as compared to the past; it keeps on changing due to the wide variety of customer needs, all thanks to increased literacy rate, globalized market, heavy competition, and availability of a number of substitute. Consumers are constantly evolving which means their tastes and preferences change with them. It is the changing consumer behavior that drives the innovation and development of products. Plus, it also counters seasonal fluctuations.

  • Explore technology

Just as consumer trends drive new products, advances in technology drives companies to invest in new products. If your company has not upgraded its technology arsenal for ten years, count yourself to be at the last one in the queue within a few years.

  • Reputation and goodwill

Building image and reputation as a dynamic innovation and creative firm boosts a company’s legacy. The new product development is approached. Company desires to convince the market that it works hard to meet customer’s expectations. In fact, company developing new products frequently has more reputation and can easily attract customers.

Industrial design is a very crucial part of the entire new product development process. We are aware of the fact that industrial design develops aspects of a product that create emotional connections with the user. It integrates all aspects of form, fit, and function, hence optimizing them to create the best possible user experience. Industrial design’s role in product development process is to establish the design language of a product, as well as the corporate branding and identity.

How successfully a company is able to carry out development or modification, incorporating the ergonomics aspect, can often determine the success of a product in the market. Firms that leave industrial design to the end of the engineering lifecycle, or out completely will struggle to find success in consumer-driven markets.

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Mesh

For those acquainted with mechanical design and reverse engineering, they can testify to the fact that the road to a new product design involves several steps. In reverse engineering, the summary of the entire process involves scanning, point cloud generation, meshing, computer-aided designing, prototyping and final production. This section covers a very crucial part of the process — Meshing or simply put, Mesh.

To put a simple definition, a mesh is a network that constitutes of cells and points.

Mesh generation is the practice of converting the given set of points into a consistent polygonal model that generates vertices, edges and faces that only meet at shared edges. It can have almost any shape in any size. Each cell of the mesh represents an individual solution, which when combined, results in a solution for the entire mesh.

 

mesh

Mesh is formed of facets which are connected to each other topologically. The topology is created using following entities:

  • Facet - A triangle connecting three data points
  • Edge - A line connecting two data points
  • Vertex - A data point
Mesh Property

Before we proceed to know the types of meshes, it is necessary to understand the various aspects that constitute a mesh. It is important to know the concept of a polygonal mesh.

A polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object in 3D graphics and solid modeling. The faces usually consist of triangles, quadrilaterals or other simple polygons as that simplifies rendering. It may also be composed of more general concave polygons or polygons with holes.

Objects created with polygon meshes must store different types of elements. These include:

  • Vertex: A position (usually in 3D space) along with other information such as color, normal vector and texture coordinates
  • Edge: A connection between two vertices
  • Face: A closed set of edges, in which a triangle face has three edges, and a quad face has four edges
  • Surfaces: They are often called smoothing groups. Generally, surfaces are not required to group smooth regions

A polygon mesh may be represented in a variety of ways, using different methods to store the vertex, edge and face data. These include:

  • Face-vertex meshes
  • Winged edge meshes
  • Corner tables
  • Vertex-vertex meshes
Types of meshes

Meshes are commonly classified into two divisions, Surface mesh and Solid mesh. Let us go through each section one by one.

Surface Mesh: A surface mesh is a representation of each individual surface constituting a volume mesh. It consists of faces (triangles) and vertices. Depending on the pre-processing software package, feature curves may be included as well.

Generally, a surface mesh should not have free edges and the edges should not be shared by two triangles.

The surface should ideally contain the following qualities of triangle faces:

  • Equilateral sized triangles
  • No sharp angles/surface folds etc. within the triangle proximity sphere
  • Gradual variation in triangle size from one to the next

The surface mesh generation process should be considered carefully. It has a direct influence on the quality of the resulting volume mesh and the effort it takes to get to this step.

surface mesh

Solid Mesh: Solid mesh, also known as volume mesh, is a polygonal representation of the interior volume of an object. There are three different types of meshing models that can be used to generate a volume mesh from a well prepared surface mesh.

The three types of meshing models are as follows:

  • Tetrahedral - tetrahedral cell shape based core mesh
  • Polyhedral - polyhedral cell shape based core mesh
  • Trimmed - trimmed hexahedral cell shape based core mesh

Once the volume mesh has been built, it can be checked for errors and exported to other packages if desired.

solid mesh

Mesh type as per Grid structure

A grid is a cuboid that covers entire mesh under consideration. Grid mainly helps in fast neighbor manipulation for a seed point.

mesh grid

Meshes can be classified into two divisions from the grid perspective, namely Structured and Unstructured mesh. Let us have a look at each of these types.

Structured Mesh: Structured meshes are meshes which exhibits a well-known pattern in which the cells are arranged. As the cells are in a particular order, the topology of such mesh is regular. Such meshes enable easy identification of neighboring cells and points, because of their formation and structure. Structured meshes are applied over rectangular, elliptical, spherical coordinate systems, thus forming a regular grid. Structured meshes are often used in CFD.

structured mesh

Unstructured Mesh: Unstructured meshes, as the name suggests, are more general and can randomly form any geometry shape. Unlike structured meshes, the connectivity pattern is not fixed hence unstructured meshes do not follow a uniform pattern. However, unstructured meshes are more flexible. Unstructured meshes are generally used in complex mechanical engineering projects.

Unstructured Mesh

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Mesh - List of operations

Good cell quality of meshes translate into accurate results within optimum time after computation. But more often than not, we get a mesh output, which is far from accuracy. There are number of factors affecting a mesh, that might compromise with the final result. This chapter focuses on the various shortcomings of a mesh and their repair algorithms.

Mesh Decimation/Simplification

Mesh decimation/simplification is the method of reducing the number of elements used in a mesh while maintaining the overall shape, volume and boundaries preserved as much as possible. It is a type of algorithm that aims to transform a given mesh into another with fewer elements (faces, edges and vertices). The decimation process usually involves a set of user-defined quality criteria, that maintains specific properties of the original mesh as much as possible. This process reduces the complexity of a mesh.

Before Mesh Decimation

 

After Mesh Decimation

 

Mesh Hole-Filling

To analyze a mesh model, it must be complete. Often, some mesh models carry holes in them, which must be filled. The unseen areas of the model appear as holes, which are aesthetically unsatisfying and can be a hindrance to algorithms that expect a continuos mesh. The Fill Hole command fills the holes and gaps in the mesh.

Note – The Fill Hole command only works on triangulated mesh and not tetrahedral mesh

Mesh Before Hole Filling

 

Mesh After Hole Filling

 

Mesh Refinement

Certain situations arise which makes us concerned about the accuracy a model in certain areas. Such scenarios prompt us to have fine mesh in those areas to ensure accurate results. However, creating a surface mesh of the entire model with a fine mesh size may ask for unnecessary hours to analyze the fine mesh in those regions where the results are not as important to you. The answer to this issue is the usage of refinement points.

A refinement point identifies a region or volume of space in which a finer mesh has to be generated. Mesh refinement can be defined by identifying an absolute size for the local mesh. Mesh refinement ends up in creating more number of elements in the specified region of the model.

Before Mesh Refinement

 

After Mesh Refinement

 

Mesh Smoothing

Mesh smoothing is also known as mesh relaxation. Sometimes it is necessary to modify that mesh after a mesh generation. It is achieved either by changing the positions of the nodes or by removing the mesh altogether. Mesh smoothing results in the modification of mesh point positions, while the topology remains as it is.

Before Mesh Smoothing

 

After Mesh Smoothing

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Mesh Quality

The quality of a mesh plays a significant role in the accuracy and stability of the numerical computation. Regardless of the type of mesh used in your domain, checking the quality of your mesh is a must. The ‘good meshes’ are the ones that produce results with fairly acceptable level of accuracy, considering that all other inputs to the model are accurate. While evaluating whether the quality of the mesh is sufficient for the problem under modeling, it is important to consider attributes such as mesh element distribution, cell shape, smoothness, and flow-field dependency.

Element Distribution

It is known that meshes are made of elements (vertices, edges and faces). The extent, to which the noticeable features such as shear layers, separated regions, shock waves, boundary layers, and mixing zones are resolved, relies on the density and distribution of mesh elements. In certain cases, critical regions with poor resolution can dramatically affect results. For example, the prediction of separation due to an adverse pressure gradient depends heavily on the resolution of the boundary layer upstream of the point of separation.

Cell Quality

The quality of a cell has a crucial impact on the accuracy of the entire mesh. The quality of cell is analyzed by the virtue of three aspects: Orthogonal quality, Aspect ratio and Skewness.

Orthogonal Quality: An important indicator of mesh quality is an entity referred to as the orthogonal quality. The worst cells will have an orthogonal quality close to 0 and the best cells will have an orthogonal quality closer to 1.

Aspect Ratio: Aspect ratio is an important indicator of mesh quality. It is a measure of stretching of the cell. It is computed as the ratio of the maximum value to the minimum value of any of the following distances: the normal distances between the cell centroid and face centroids and the distances between the cell centroid and nodes.

Skewness: Skewness can be defined as the difference between the shape of the cell and the shape of an equilateral cell of equivalent volume. Highly skewed cells can decrease accuracy and destabilize the solution.

Smoothness

Smoothness redirects to truncation error which is the difference between the partial derivatives in the equations and their discrete approximations. Rapid changes in cell volume between adjacent cells results in larger truncation errors. Smoothness can be improved by refining the mesh based on the change in cell volume or the gradient of cell volume.

Flow-Field Dependency

The entire effects of resolution, smoothness, and cell shape on the accuracy and stability of the solution process is dependent upon the flow field being simulated. For example, skewed cells can be acceptable in benign flow regions, but they can be very damaging in regions with strong flow gradients.

Correct Mesh Size

Mesh size stands out as one of the most common problems to an equation. The bigger elements yield bad results. On the other hand, smaller elements make computing so long that it takes a long amount of time to get any result. One might never really know where exactly is the mesh size is on the scale.

It is important to consider chosen analysis for different mesh sizes. As smaller mesh means a significant amount of computing time, it is important to strike a balance between computing time and accuracy. Too coarse mesh leads to erroneous results. In places where big deformations/stresses/instabilities take place, reducing element sizes allow for greatly increased accuracy without great expense in computing time.

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Meshing Algorithms

In the previous session, we have learned what Mesh is and the various aspects upon which a mesh can be classified. Mesh generation requires expertise in the areas of meshing algorithms, geometric design, computational geometry, computational physics, numerical analysis, scientific visualization and software engineering to create a mesh tool.

Over the years, mesh generation technology has evolved shoulder to shoulder with increasing hardware capability. Even with the fully automatic mesh generators there are many cases where the solution time is less than the meshing time. Meshing can be used for wide array of applications, however the principal application of interest is the finite element method. Surface domains are divided into triangular or quadrilateral elements, while volume domain is divided mainly into tetrahedral or hexahedral elements. A meshing algorithm can ideally define the shape and distribution of the elements.

A key step of the finite element method for numerical computation is mesh generation algorithms. A given domain is to be partitioned it into simpler ‘elements’. There should be few elements, but some portions of the domain may need small elements so that the computation is more accurate there. All elements should be ‘well shaped’. Let us take a walkthrough of different meshing algorithms based of two common domains, namely quadrilateral/hexahedral mesh and triangle/tetrahedral mesh.

Algorithm methods for Quadrilateral or Hexahedral Mesh

Grid-Based Method

The grid based method involves the following steps:

  • A user defined grid is fitted on 2D & 3D object. It generates quad/ hex elements on the interior of the object.
  • Some patterns are defined for boundary elements followed by forming a boundary element by applying boundary intersection grid.
  • This results in the generation of quadrilateral mesh model.

Mesh Grid based method

 

Medial Axis Method

Medial axis method involves an initial decomposition of the volumes. The method involves few steps as given below:

  • Consider a 2D object with hole.
  • A maximal circle is rolled through the model and the centre of circle traces the medial object.
  • Medial object is used as a tool for automatically decomposing the model in to simple meshable region.
  • Series of templates for the region are formed by the medial axis method to fill the area with quad element.

Mesh Medial axis method

 

Plastering method

Plastering is the process in which elements are placed starting with the boundaries and advancing towards the centre of the volume. The steps of this method are as follows:

  • A 3D object is taken.
  • One hexahedral element is placed at boundary.
  • Individual hexahedral elements are projected towards the interior of the volume to form hexahedral meshing, row by row and element by element.
  • The process is repeated until mesh generation is completed.

Mesh Plastering method

 

Whisker Weaving Method

Whisker weaving is based on the concept of the spatial twist continuum (STC). The STC is the dual of the hexahedral mesh, represented by an arrangement of intersecting surfaces, which bisect hexahedral elements in each direction. The whisker weaving algorithm can be explained as in the following steps:

  • The first step is to construct the STC or dual of the hex mesh.
  • With a complete STC, the hex elements can then be fitted into the volume using the STC as a guide. The loops can be easily determined from an initial quad mesh of the surface.
  • Hexes are then formed inside the volume, once a valid topological representation of the twist planes is achieved. One hex is formed wherever three twist planes converge.

Mesh Whisker weaving method

 

Paving Method

The paving method has the following steps to generate a quadrilateral mesh:

  • Initially a 2D object is taken.
  • A node is inserted in the boundary and the boundary node is considered as loop.
  • A quadrilateral element is inserted and a row of elements is formed.
  • The row of element is placed around the boundary nodes.
  • Again this same procedure adopt for next rows.
  • Finally quad mesh model is formed.

Mesh Paving method

Mesh Paving method

 

Mapping Mesh Method

The Mapped method for quad mesh generation involves the following steps:

  • A 2D object is taken.
  • The 2D object is split into two parts.
  • Each part is either a simple 2D rectangular or a square object.
  • The simple shape object is unit meshed.
  • The unit meshed simple shape object is mapped in its original form and then joined back to form actual object.

Mapping mesh method

Mapping mesh method

 

Algorithm methods for Triangular and Tetrahedral Mesh

Quadtree Mesh Method

With the quadtree mesh method, square containing the geometric model are recursively subdivided until the desired resolution is reached. The steps for two dimensional quadtree decomposition of a model are as follows:

  • A 2D object is taken.
  • The 2D object is divided into rectangular parts.
  • A Detail tree of divided object is provided.
  • The object is eventually converted into triangle mesh.

 Quadtree mesh method

 

Delaunay Triangulation Method

A Delaunay triangulation for a set P of discrete points in the plane is a triangulation DT such that no points in P are inside the circum-circle of any triangles in DT. The steps of construction Delaunay triangulation are as follows:

  • The first step is to consider some coordinate points or nodes in space.
  • The condition of valid or invalid triangle is tested in every three points which finds some valid triangle to make a triangular element.
  • Finally a triangular mesh model is obtained.

Delaunay Triangulation maximizes the minimum angle of all the angle of triangle and it tends to avoid skinny triangles.

Mesh Delaunay Triangulation method

Mesh Delaunay Triangulation method

 

Advancing Front Method

Another very popular family of triangular and tetrahedral mesh generation algorithms is the advancing front method, or moving front method. The mesh generation process is explained as following steps:

  • A 2D object with a hole is taken.
  • An inner and outer boundary node is inserted. The node spacing is determined by the user.
  • An edge is inserted to connect the nodes.
  • To start the meshing process, an edge AB is selected and a perpendicular is drawn from the midpoint of AB to point C (where C is node spacing determined by the user) in order to make a triangular element.
  • After one element is generated, another edge is selected as AB and a point C is made, but if in case any other node lets point D within the defined radius, then ABC element is cancelled and instead, an element ABD is formed.
  • This process is repeated until mesh is generated.

Mesh Advancing Front method

 

Spatial Decomposition Method

The steps for spatial decomposition method are as follows:

  • Initially a 2D object is taken.
  • The 2D object is divided into minute parts till we get the refined triangular mesh.

Mesh Spatial Decomposition method

 

Sphere Packing Method

The sphere packing method follows the given steps:

  • Before constructing a mesh, the domain is filled with circles.
  • The circles are packed closely together, so that the gaps between them are surrounded by three or four tangent circles.
  • These circles are then used as a framework to construct the mesh, by placing mesh vertices at circle centers, points of tangency, and within each gap while using generated points. Eventually, the triangular mesh is generated.

Mesh Sphere Packing method

Mesh Sphere Packing method

 

 

 

 Source

Singh, Dr. Lokesh, (2015). A Review on Mesh Generation Algorithms. Retrieved from http://www.ijrame.com

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