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.

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.

 

The art of metalworking has a primary concern, locating the part to be machined relative to the platform. A CNC machine starts machining at a specific point corresponding to the fixture and proceeds from there. Therefore, the preciseness with which a job is machined is dependent on the accuracy that holds in the fixture. The accurate location of every part loaded into the fixture is essential. Any deviation in part location adds to the dimensional tolerance that must be assigned to the finished pieces. Furthermore, improper supporting and securing the part in the fixture affects surface finishes by temporarily or permanently deforming it. Hence, techniques for supporting, clamping, and locating must be considered together to assure repeatability from part to part.

Basic principles of Jigs and Fixtures design

LOCATING POINTS: Locating the work is a prime necessity and requires suitable facilities. The correct setup ensures smooth insertion of a workpiece in the proper position and removing a workpiece from a jig without operational hassles or time consumption. The workpiece position needs to be precise with the guiding tool in the jig or setup pieces in the fixture.

FOOLPROOF: A foolproof design of jigs and fixtures does not permit a tool or workpiece to be placed in any other way other than the intended one.

REDUCTION OF IDLE TIME: Jigs and Fixtures must be designed in such a way that ensures smooth loading, clamping, machining, and unloading of a

WEIGHT OF JIGS AND FIXTURES: A jig and fixture must be compact, easy to handle, and low cost regarding the number of materials used without giving up stiffness and rigidity.

JIGS PROVIDED WITH FEET: Some jigs require feet so that they can be placed on the table firmly.

MATERIALS FOR JIGS AND FIXTURES: Jigs and Fixtures are usually created with hardened materials to resist wear & tear and avoid frequent damage—for example, Mild steel, Cast iron, Die steel, High-speed steel, Caesium.

CLAMPING DEVICE: A suitable clamp is rated for its strength. It should be able to hold a workpiece firmly in its position while bearing the strain of the cutting tool simultaneously, without springing.

Broad rules of Jigs & Fixtures Design

• Compare the production cost of work between the existing tools and the tool to be made and see if the manufacturing price is not more than the expected gain.
• Determine location points and outline clamping arrangement.
• Make sure the clamping and binding pieces are as quick to act & efficient as possible.
• Make the jig and fixture foolproof.
• Make sure the locating points are adjustable.
• Do avoid intricate clamping arrangements.
• Round all corners.
• Make sure the operator has handles to make handling tasks easier.
• Provide ample amount of clearance.
• Provide holes for chips to escape.
• Systematically locate clamps to resist the pressure of the cutting tool while machining.
• To avoid springing action, place all clamps in proximity opposite to the bearing point of the workpiece.
• Test the jigs before putting them in a shop.

The 3-2-1 principle

Locating a part to be machined involves mainly three steps: Supporting, Positioning, and Clamping.

Two main intentions when placing a job on a jig/fixture are:

• Precisely positioning the part at the desired coordinates.
• Curbing all six degrees of movement so that the part cannot budge.

An extensively used method for obtaining these objectives is the 3-2-1 principle or six degrees of freedom for part location.

 

Image Source: Quora

The 3-2-1 method is a work-holding principle where three pins are located on the 1st principle plane, i.e., either XY, YZ, ZX. And two pins are located on the 2nd plane perpendicular to the 1st plane, and at last, one pin on the plane is mutually perpendicular to the 1st and 2nd planes. The aim is to constrain the movement of the workpiece along all three axes.

Design objectives of Jigs and Fixtures

Before sitting down to design jigs/fixtures, the designer must consider the following points:

• The tool must be foolproof to prevent any mishandling or accidental usage by the operator.
• Easy to operate for increasing efficiency.
• Easy to manufacture using the lowest costs.
• Its ability to weather the tool life instead of appropriate materials.
• Must be consistent at producing high-quality parts.
• Must be safe and secure to use.

The designer must know the basics of the process and the tools associated with it for which the jig/fixture is designed. Overall objectives to look out for a while developing such tools are:

• Cycle time.
• Type of Jig/Fixture.
• Part Assembly sequence or Machining locations.
• Joining or machining process.
• Clamping method and clamping sequence.
• Required output accuracy.
• Type of equipment to be used with the jig.
• Method of ejecting finished output and transferring it to the next. Platform, whether the manual or automatic mode.
• The type of material, recommended weight, number of spots involving welding.

Reference: National Institute of Technology, Calicut

 

The design of jigs and fixtures is dependent on numerous factors which are analysed to achieve optimum output. Jigs should be made of rigid light materials to facilitate secure handling, as it has to be rotated severally to enable holes to be drilled from different angles. It is recommended that four feet should be provided for jigs that are not bolted on the machine tool, to enable the jig to wobble if not well positioned on the table and thereby alert the operator. Drill jigs provide procedures for proper location of the work-piece concerning the cutting tool, tightly clamp and rigidly support the work-piece during machining, and also guide the tool position and fasten the jig on the machine tool.

To achieve their expected objectives, jigs and fixtures consist of many elements:

• Frame or body and base which has features for clamping
• The accuracy and availability of indexing systems or plates
• The extent of automation, capacity, and type of machine tool where jigs and fixtures will be employed
• Bushes and tool guiding frames for jigs
• The availability of locating devices in the machine for blank orientation and suitable positioning
• Auxiliary elements
• The strength of the machine tool under consideration
• The precision level of the expected product
• Fastening parts
• The available safety mechanisms in the machine tool
• The study of the fluctuation level of the machine tool

 

 

The factors below are to be reflected upon during design, production, and assembly of jigs and fixtures due to the targeted increase in throughput, quality of products, interchangeability, and more accuracy.

• Guiding of tools for slim cutting tools like drills
• Type of operations
• Inspection requirements
• Provision of reliable, rigid, and robust reinforcement to the blank
• Production of jigs and fixtures with a minimum number of parts
• Fast and accurate location of the jig or fixture blank
• Rapid mounting and un-mounting of the work-piece from the jig or fixture
• Set up time reduction
• Standard and quality parts must be used
• Reduction of lead time
• Easy disposal of chips
• Enhanced flexibility

Elements of Jigs and Fixtures

The significant features of Jigs and Fixtures are:

The body: The body is the most outstanding element of jigs and fixtures. It is constructed by welding of different slabs and metals. After the fabrication, it is often heat-treated for stress reduction as its main objective is to accommodate and support the job.

Clamping devices: The clamping devices must be straightforward and easy to operate, without sacrificing efficiency and effectiveness. Apart from holding the work-piece firmly in place, the clamping devices are capable of withholding the strain of the cutting tool during operations. The need for clamping the work-piece on the jig or fixture is to apply pressure and press it against the locating components, thereby fastening it in the right position for the cutting tools.

Locating devices: Thepin is the most popular device applied for the location of work-piece in jigs and fixtures.The pin’s shank is press-fitted or driven into a jig or fixture. The locating width of the pin is made bigger than the shank to stop it from being pressed into the jig or fixture body because of the weight of the cutting tools or work-piece. It is made with hardened steel.

Jig bushing or tool guide:Guiding parts like jig bushings and templates are used to locate the cutting tool relative to the component being machined. Jig bushes are applied in drilling and boring, which must be wear resistant, interchangeable, and precise. Bushes are mainly made of a reliable grade of tool steel to ensure hardening at a low temperature and also reduce the risk of fire crackling.

 

 

Selection of Materials

There is a wide range of materials from where jigs and fixtures could be made, to resist tear and wear, the materials are often tempered and hardened. Also, phosphor bronze and other non-ferrous metals, as well as composites, and nylons for wear reduction of the mating parts, and damage prevention to the manufacturing part is used. Some of the materials are discussed below:

• Phosphor Bronze: phosphor bronze is used in the production of jigs and fixtures for processes that involve making of interchangeable nuts in clamping systems like vices, and also incorporated feedings that require screws. As the manufacturing of screws is costly and also wastes a lot of time, the reduction of their tear and wear is often achieved by using replaceable bronze mating nuts made with phosphor bronze.

• Die Steels: the three variants of die steel - high chromium (12 %), high carbon (1.5 to 2.3%), and cold working steels are applied in the production of jigs and fixtures for the making of thread forming rolls, as well as cutting of press tools. When alloyed with vanadium and molybdenum for it to retain toughness at very high temperature, die steels are applied in the fabrication of jigs and fixtures that are used in high-temperature work processes which include extrusion, forging, and casting processes.

• High-Speed Steels: High-speed steels which contain more quantity of tungsten and less quantity of chromium and vanadium have high toughness, hardness retention at high temperature, and excellent wear, tear and impact resistance. When tempered, they are applied in the production of jigs and fixtures for reaming, drilling, boring, and cutting operations.

• Carbon Steels: when tempered with oil, carbon steels are applied in the making of some jig and fixture parts which are exposed to tear and wear like the locators and jig bushes.

• Mild steels: Mild steel, which contains about 0.29% of Carbon, is very cheap and because of their easy availability is often the choicest material for the making of jigs of fixtures.

Other materials for the making of jigs and fixtures include Nylon and Fibre, steel castings, stainless steel, cast iron, high tensile steels, case hardening steels, and spring steels.

Reference

Charles ChikwenduOkpala, EzeanyimOkechukwu C “The Design and Need for Jigs and Fixtures in Manufacturing” Science Research.Vol. 3, No. 4, 2015, pp. 213-219. DOI: 10.11648/j.sr.20150304.19

Reverse engineering found its use in various industries gradually, as more and more industry leaders adopted this approach and implemented the same, thereby easing out their own work-process. Here is a list of industries that use reverse engineering as a part of their methods:

• Manufacturing/Heavy machine
• Automotive
• Software development
• Military projects
• Space expeditions
• Aerospace
• Architecture
• Oil & gas

The future

It is the 21st century. These are great times for design engineers. Over the past two decades, their job has been dramatically changed, with the transformation of finite element analysis (FEA) software from mainframe to desktop computer. With the easy availability of computer-aided design software packages, reverse engineering technology has become a practical means to create a 3D virtual model of an existing physical part. That, in turn, has made the use of 3D CAD, CAM, or other CAE applications easier.

The convenience in the usage, affordability and the ability of its software to tightly integrate with a CAD program has made this process a much favored among engineers. At the same time, the costs of scanners and other hardware used to input measurements have been dropping, and the hardware is becoming smaller and easier to use, according to the hardware makers.

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.

 

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.

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.

 

 

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 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.

 

 

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.

 

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.

 

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.

 

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.

 

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.

 

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.

 

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.

 

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.

 

 

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.

 

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.

 

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.

 

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.

 

 

 

 Source

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

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.