Engineering analysis with/pro- mechanica and ansys free pdf download

Only the components in the band region around the diagonal of the matrix are non-zero and the others are zero. Due to this nature, the coefficient matrix is called the sparse or band matrix. From the boundary conditions, the values of u1 and u4 in the left-hand side of Equation 1. In this section, only one-dimensional FEM was described. The FEM can be applied to two- and three-dimensional continuum problems of various kinds which are described in terms of ordinary and partial differential equations.

There is no essen- tial difference between the formulation for one-dimensional problems and the formulations for higher dimensions except for the intricacy of formulation. The exact solutions can be obtained in quite limited cases only and in general cannot be solved in closed forms. In order to overcome these difficulties, the FEM has been developed as one of the powerful numerical methods to obtain approximate solutions for various kinds of elasticity problems.

The FEM assumes an object of analysis as an aggregate of ele- ments having arbitrary shapes and finite sizes called finite element , approximates partial differential equations by simultaneous algebraic equations, and numerically solves various elasticity problems.

Finite elements take the form of line segment in one-dimensional problems as shown in the preceding section, triangle or rectangle in two-dimensional problems, and tetrahedron, cuboid, or prism in three-dimensional problems.

Since the procedure of the FEM is mathematically based on the variational method, it can be applied not only to elasticity problems of structures but also to various problems related to thermodynamics, fluid dynamics, and vibrations which are described by partial differential equations.

The solutions for unknown forces are reaction forces and those for unknown displacements are deformations of the elastic body of interest for given geometrical and mechanical boundary conditions, respectively. Unlike the other fundamental equations shown in Equations 1. The plane stress approximation satisfies the equations of equilibrium 1. Strictly speaking, the plane stress state does not exist in reality. This case is called the plane stress approximation.

Since the plane strain state satisfies the equa- tions of equilibrium 1. These conditions are called boundary conditions. There are two types of boundary conditions, i. Note that it is not possible to prescribe both stresses and displacements on a portion of the surface of the elastic body. Ss 2e e 3e 1e D Su Figure 1. One of the most popular geometrical boundary conditions, i.

The first term in the left-hand side of Equation 1. Therefore, Equation 1. The fact that the integrand in each integral in the left-hand side of Equation 1.

Therefore, instead of solving the partial differential equations 1. Since the boundaries between neighboring elements are straight lines joining the apices or nodal points of triangular elements, incompatibility does not occur along the bound- aries between adjacent elements and displacements are continuous everywhere in the domain to be analyzed as shown in Figure 1.

Nodal points should be numbered counterclockwise. These three numbers are used only in the eth element. Nodal numbers of the other type called global nodal numbers are also assigned to the three nodal points of the eth element, being num- bered throughout the whole model of the elastic body.

Equation 1. Now, let us consider strains derived from the displacements given by Equation 1. Substitution of Equation 1. All the components of the [B] matrix are expressed only by the coordinate values of the three nodal points consisting of the element. From the above discussion, it can be concluded that strains are constant through- out a three-node triangular element, since its interpolation functions are linear functions of the coordinate variables within the element.

Three-node triangular elements cannot satisfy the compatibility condition in the strict sense, since strains are discontinuous among elements. It is demonstrated, however, that the results obtained by elements of this type converge to exact solutions as the size of the elements becomes smaller. It is known that elements must fulfill the following three criteria for the finite- element solutions to converge to the exact solutions as the subdivision into even- smaller elements is attempted.

Namely, the elements must 1 represent rigid body displacements, 2 represent constant strains, and 3 ensure the continuity of displacements among elements. The matrix [De ] is for elastic bodies and thus is called the elastic stress— strain matrix or just [D] matrix. In order to make differentiations shown in Equation 1. The remaining conditions to be satisfied are the equations of equilibrium 1. Hence, the equivalent nodal forces, for instance X1e , Y1e , X2e , Y2e , and X3e , Y3e , are defined on the three nodal points of the eth element via determining these forces by the principle of the virtual work in order to satisfy the equilibrium and boundary conditions element by ele- ment.

Since the integrand in Equation 1. Since nodal points which belong to different elements but have the same coordinates are the same points, the following items during the assembly procedure of the global stiffness equations are to be noted: 1 The displacement components u and v of the same nodal points which belong to different elements are the same; i.

The same global nodal numbers are to be assigned to the nodal points which have the same coordinates. Taking the items described above into consideration, let us rewrite the element stiffness matrix [k e ] in Equation 1.

This procedure is called the method of extended matrix. The number of degrees of freedom here means the number of unknown variables.

In two-dimensional elasticity problems, since two of displace- ments and forces in the x- and the y-directions are unknown variables for one nodal point, every nodal point has two degrees of freedom.

Hence, the number of degrees of freedom for a finite-element model consisting of n nodal points is 2n. The values of XI in Equation 1. The square plate model has a side of unit length 1 and a thickness of unit length 1, and consists of two constant- strain triangular elements, i. Let us determine the element stiffness matrix for Element 1. After multiplication of the matrices in Equation 1. The components of the nodal displacement and force vectors are written by the element nodal numbers. By rewriting these components by the global nodal numbers as shown in Figure 1.

Let us now impose boundary conditions on the nodes. Substitution of Equations 1. The solutions for Equation 1. The strains and stresses in the square plate can be calculated by substituting the solutions 1.

It is concluded that the above results obtained by the FEM agree well with the physical interpretations of the present problem.

Bibliography 1. Zienkiewicz and K. Zienkiewicz and R. Bibliography 35 3. Rowe et al. Dym and I. Yagawa et al. Washizu et al. In general, a finite-element solution may be broken into the following three stages.

The first is by means of the graphical user interface or GUI. This method follows the conventions of popular Windows and X-Windows based programs. The GUI method is exclusively used in this book. The second is by means of command files. The command file approach has a steeper learning curve for many, but it has the advantage that the entire analysis can be described in a small text file, typically in less than 50 lines of commands.

This approach enables easy model modifications and minimal file space requirements. Within the Main Window there are five divisions see Figure 2. More push buttons can be made available if desired. It is from this menu that the vast majority of modeling commands are issued. It is here where the model in its various stages of construction and the ensuing results from the analysis can be viewed. The Output Window, shown in Figure 2. It is usually positioned behind the Graphics Window and can be put to the front if necessary.

Figure 2. Very often the stage in the modeling is reached where things have gone well and the model ought to be saved at this point. In that way, if mistakes are made later on, it will be possible to come back to this point.

The model will be saved in a file called Jobname. It is a good idea to save the job at different times throughout the building and analysis of the model to backup the work in case of a system crash or other unforeseen problems. In response to the second option frame, shown in Figure 2. B C A Figure 2. Select appropriate drive [A] and give the file a name [B]. Clicking [C] OK button saves the model as a database with the name given.

There are two methods to do this: 1 Using the Launcher. This will restore as much of the database geometry, loads, solution, etc. Select appropriate file from the list [A] and click [B] OK button to resume the analysis. If a jobname is specified, say Beam, then the created files will all have the file prefix, Beam again with various extensions: beam.

This file stores the geometry, boundary conditions, and any solutions. Listing of all error and warning messages.

Depending on the operations carried out, other files may have been written. These files may contain, for example, results. If the GUI is always used, then only the.

Once the ANSYS program has started, and the job name has been specified, only the resume command has to be activated to proceed from where the model was last left off. The log file contains a complete list of the ANSYS commands used to get the model to its current stage.

That file may be run as is, or edited and rerun as desired. However, it is often desired to save the results to a file to be later analyzed or included in a report. In case of stresses, instead of using Plot Results to plot the stresses, choose List Results.

In the same way as described above. When the list appears on the screen in its own window, select File: Save As and give a file name to store the results.

Any other solution can be done in the same way. For example, select Nodal Solution from the List Results menu to get displacements. Save the resulting list in the same way described above. There are two options, namely To Printer see Figure 2. In the frame shown in Figure 2. Then enter an appropriate file name and click [E] OK button.

This image file may now be printed on a PostScript printer or included in a document. A frame shown in Figure 2. A Figure 2. There are four options, depending on what is important to be saved. If nothing is to be saved then select [A] Quite — No Save as indicated. Building a finite-element model requires more time than any other part of the analysis. First, a jobname and analysis title have to be specified.

Next, the PREP7 preprocessor is used to define the element types, element real constants, material properties, and the model geometry. Except in magnetic field analyses, any system of units can be used so long as it is ensured that units are consistent for all input data.

Each element type has a unique number and a prefix that identifies the element category. In order to define element types, one must be in PREP7. In response, the frame shown in Figure 2. Click on [A] Add button and a new frame, shown in Figure 2. Select an appropriate element type for the analysis performed, e. Element real constants are properties that depend on the element type, such as cross-sectional properties of a beam element.

As with element types, each set of real constant has a reference number and the table of reference number versus real constant set is called the real constant table. Not all element types require real constant, and different elements of the same type may have different real constant values. A B Figure 2. According to Figure 2. Other element attributes can be defined as required by the type of analysis per- formed.

Chapter 7 contains sample problems where elements attributes are defined in accordance with the requirements of the problem. Depending on the appli- cation, material properties may be linear or nonlinear, isotropic, orthotropic or anisotropic, constant temperature or temperature dependent. As with element types and real constants, each set of material properties has a material reference number.

The table of material reference numbers versus material property sets is called the material table. In one analysis there may be multiple material property sets corre- sponding with multiple materials used in the model. Each set is identified with a unique reference number. Each material property set has its own library file. The material library files also make it possible for several users to share commonly used material property data.

In order to create an archival material library file, the following steps should be followed: i Tell the ANSYS program what system of units is going to be used.

As shown in Figure 2. Clicking twice on [A] Isotropic calls up another frame shown in Figure 2. Enter data characterizing the material to be used in the analysis into appropriate field.

If the problem requires a number of different materials to be used, then the above procedure should be repeated and another material model created with appropriate material number allocated by the program. With solid modeling, the geometry of shape of the model is described, and then the ANSYS program automatically meshes the geometry with nodes and elements.

The size and shape of the elements that the program creates can be controlled. With direct generation, the location of each node and the connectivity of each element is manually defined. Several convenience operations, such as copying patterns of existing nodes and elements, symmetry reflection, etc.

Solved example problems in this book amply illustrate, in a step-by-step manner, how to create the model geometry. Regardless of the chosen strategy, it is necessary to define the analysis type and analysis options, apply loads, specify load step options, and initiate the finite-element solution. The analysis type to be used is based on the loading conditions and the response which is wished to calculate.

For example, if natural frequencies and mode shapes are to be calculated, then a modal analysis ought to be chosen. The ANSYS pro- gram offers the following analysis types: static or steady-state , transient, harmonic, modal, spectrum, buckling, and substructuring.

Not all analysis types are valid for all disciplines. Modal analysis, for instance, is not valid for thermal models. Analy- sis options allow for customization of analysis type. Typical analysis options are the method of solution, stress stiffening on or off, and Newton—Raphson options. In response to the selection, the frame shown in Figure 2. Select the type of analysis that is appropriate for the problem at hand by activating [A] Static button for example.

The word loads used here includes boundary conditions, i. It also includes other externally and internally applied loads. Loads in the ANSYS program are divided into six categories: DOF constraints, forces, surface loads, body loads, inertia loads, and coupled field loads.

Most of these loads can be applied either on the solid model keypoints, lines, and areas or the finite-element model nodes and elements. There are two important load-related terms. A load step is simply a configuration of loads for which the solution is obtained.

In a structural analysis, for instance, wind loads may be applied in one load step and gravity in a second load step. Load steps are also useful in dividing a transient load history curve into several segments. Substeps are incremental steps taken within a load step. They are mainly used for accuracy and convergence purposes in transient and nonlinear analyses. Substeps are also known as time steps which are taken over a period of time. Load step options are alternatives that can be changed from load step to load step, such as number of substeps, time at the end of a load step, and output controls.

Depending on the type of analysis performed, load step options may or may not be required. Sample problems solved here provide practical guide to appropriate load step options as necessary. After reviewing the summary information about the model, click [A] OK button to start the solution.

When this command is issued, the ANSYS program takes model and loading information from the database and calculates the results. Results are written to the results file and also to the database.

The only difference is that only one set of results can reside in the database at one time, while a number of result sets can be written to the results file.

Using this postprocessor contour displays, deformed shapes, and tabular listings to review and interpret the results of the analysis can be obtained. POST1 offers many other capabilities, including error estimation, load case combinations, calculations among results data, and path operations. Graph plots of results data versus time or frequency and tabular listings can be obtained.

Other POST26 capabilities include arithmetic calculations and complex algebra. Beams are also used as shafts in cars and trains, as wings in aircrafts and bookshelves in bookstores.

Arms and femurs of human beings and branches of trees are good examples of portions of living creatures which support their bodies. Beams play important roles not only in inorganic but also in organic structures. Mechanics of beams is one of the most important subjects in engineering. P Modeling Figure 3. Point load a b c 5 mm d e f 10 mm 20 40 60 80 Cross section x mm Figure 3. In this chapter, the analytical procedures will be explained following the flowchart illustrated in Figure 3.

Figure 3. After carrying out the operations above, a window called Rectangle by 2 corners as shown in Figure 3. This procedure can be performed any time before the solution procedure, for instance, after setting boundary conditions. If this procedure is missed, we cannot perform the solution procedure. B C D Figure 3. The procedures for finite- element discretization are firstly to select the element type, secondly to input the element thickness and finally to divide the beam area into elements.

Click [H] Close button to close the window. E A H Figure 3. C B D Figure 3. F G Figure 3. The beam area is divided into these 8-node rectangular 82 finite elements. Click [C] OK button. B C Figure 3. Click [F] Close button, which makes the oper- ation of setting the plate thickness completed. By the operations above the element size of 0. Move this arrow to the beam area and click this area to mesh. Click [A] OK button to see the area meshed by 8-node rectangular isoparametric finite elements as shown in Figure 3.

A Figure 3. How to modify meshing In case of modifying meshing, delete the elements, and repeat the procedures [1] through [4] above. Repeat from the procedures [1], from [2] or from [3] for modifying the element type, for changing the plate thickness without changing the element type, or for changing the element size only. Move this arrow to the beam area and click this area. Click OK button to delete the elements from the beam area.

After this operation, the area disappears from the display. Execute the following commands to replot the area.

Display the nodes first to define the constraint and loading conditions. The Pan-Zoom-Rotate window opens as shown in Figure 3. Click the upper left point and then the lower right point which enclose a portion of the beam area to enlarge as shown in Figure 3.

Zoom in the left end of the beam. ROT on Nodes window opens as shown in Figure 3. How to reselect nodes Click [D] Reset button to Figure 3. OK button in the procedure 2 above, and repeat the procedures 1 and 2 above. Imposing constraint conditions on nodes The Apply U. ROT on Nodes window see Figure 3. A B Figure 3. Similarly, the selection of UX makes the displacement in the x-direction equal to zero and the selection of UY makes the displacement in the y-direction equal to zero.

The upright triangles indicate that each node to which the triangular symbol is attached is fixed in the y-direction, whereas the tilted triangles indicate the fixed condition in the x-direction. Select UX and UY to delete the constraints in the x- and the y-directions, respectively. How to cancel the selection of the nodes of load application Click Reset button before clicking OK button or click the right button of the mouse to change the upward arrow to the downward arrow and click the yellow frame.

The yellow frame disappears and the selection of the node s of load application is canceled. A positive value for load indicates load in the upward or rightward direction, whereas a negative value load in the downward or leftward direction. A B C Figure 3. B Figure 3. Click [C] Close button to close the window. The DMX value shown in the Graphics window indicates the maximum deflection of the beam.

Select [E] All applicable in the Number of facets per element edge box to calculate stresses and strains at middle points of the elements. The results obtained by three different methods agree well with one another. As the applied load increases, however, errors among the three groups of the results become larger, especially at the clamped end. This tendency arises from the fact that the clamped condition can be hardly realized in the strict sense.

Answer: 0. Choose an element size of 1 mm. If the beam shown in Figure P3. Problem 3. A half model can achieve the efficiency of finite-element calculations. This beam is the half model of the beam of Problem 3. Refer to the Appendix to create the stepped beam. Answer: Refer to the Appendix to create the stepped beam with a rounded fillet. Click [A] OK window. The color of the unpicked area s turns pink into light blue and the selection of the area s is canceled. Click [A] OK button.

Venant 3. Venant 85 Perform an FEM analysis of a 2-D elastic strip subjected to a distributed stress in the longitudinal direction at one end and clamped at the other end shown in Figure 3.

Boundary conditions: The elastic strip is subjected to a triangular distribution of stress in the longitudinal direction at the right end and clamped to a rigid wall at the left end. You must decide what kind of units to use in finite-element analyses. You can choose any system of unit you would like to, but your unit system must be consistent throughout the analyses. Click the Close button in the Element Types window to close the window. Click the OK button. Input a strip thickness of 10 mm in the Thickness box and click the OK button.

Click the Close button. Move this arrow to the elastic strip area and click this area. Click the OK button to see the area meshed by 8-node rectangular isoparametric finite elements. ROT on Lines window. Venant 89 of pressure which are symmetric to each other with respect to the center line of the strip area. Then, click the OK button. Remember that the right-end side of the strip area was divided into two lines in Procedure [4] in the preceding Section 3. Note that the values to input in the lower two boxes in the Apply PRES on Lines window is interchanged, since the distributed pressure on the lower line of the right-end side of the strip area is symmetric to that on the upper line with respect to the center line of the strip area.

The total amount of stress in any cross section is the same, i. The above result is known as the principle of St. Venant and is very useful in practice, or in the design of structural components. Namely, even if the stress dis- tribution is very complicated at the loading points due to the complicated shape of load transfer equipment, one can assume a uniform stress distribution in the main parts of structural components or machine elements at some distance from the load transfer equipment.

Observe the variation of the longitudinal stress distribution in the ligament between the foot of the hole and the edge of the plate. Elliptic hole: An elliptic hole has a minor radius of 5 mm in the longitudinal direction and a major radius of 10 mm in the transversal direction. The quarter model can be created by a slender rectangular area from which an elliptic area is subtracted by using the Boolean operation described in Section A3.

Then, create a circular area having a diameter of 10 mm and then reduce its diameter in the longitudinal direction to a half of the original value to get the elliptic area. Move the arrow to the circular area and pick it by clicking the left button of the mouse.

The color of the circular area turns from light blue into pink and click [A] OK button. An elliptic area appears and the circular area still remains. The circular area is an afterimage and does not exist in reality. Subtract the elliptic area from the rectangular area in a similar manner as described in Section A3.

Click the OK button to subtract the elliptic area from the rectangular area to get a quarter model of a plate with an elliptic hole in its center as shown in Figure 3. Move this arrow to the quarter plate area and click this area. Click the OK button to see the area meshed by 8-node isoparametric finite elements as shown in Figure 3.

Repeat the commands and operations 1 through 3 above for the bottom side of the model. Click the Close button to close the Note window. The Symbols window opens as shown in Figure 3. The reaction force is indicated by the leftward red arrows, whereas the longitudinal stress by the rightward red arrows in the ligament region. This tendency can be explained by the principle of St. Venant as discussed in the previous section. In a finite plate, the maximum stress at the foot of the hole is increased due to the finite boundary of the plate.

From Figure 3. Hence, the relative error of the present calculation is approximately, 4. Venant in the previous section. The center-cracked tension plate is assumed to be in the plane strain condition in the present analysis. Boundary conditions: The elastic plate is subjected to a uniform tensile stress in the longitudinal direction at the right end and clamped to a rigid wall at the left end. A singular element, however, has the midpoint moved one-quarter side distance from the original mid- point position to the node which is placed at the crack tip position.

This is the reason why the singular element is often called the quarter point element instead. ANSYS software is equipped only with a 2-D triangular singular element, but neither with 2-D rectangular nor with 3-D singular elements. Around the node at the crack tip, a circular area is created and is divided into a designated number of triangular singular elements.

Each triangular singular element has its vertex placed at the crack tip posi- tion and has the quarter points on the two sides joining the vertex and the other two nodes. In order to create the singular elements, the plate area must be created via key- points set at the four corner points and at the crack tip position on the left-end side of the quarter plate area. In the present model, let us create Key points 1 to 5 at the coordinates 0, 0, 0 , , 0, 0 , , 50, 0 , 0, 50, 0 , and 0, 10, 0 , respectively.

Note that the z-coordinate is always 0 in 2-D elasticity problems. Move this arrow to Key point 1 and click this point. Click Key points 1 through 5 one by one counterclockwise see Figure 3. Select the Plane strain item in the Element behavior box and click the OK button to return to the Element Types window.

Then click the OK button in the Concentration Keypoint window. Refer to the explanations of the numerical data described after the names of the respective boxes on the window. The size of the meshes other than the singular elements and the elements adjacent to them can be controlled by the same procedures as have been described in the previous sections of the present Chapter 3.

Click [A] Close button and proceed to the next operation below. Proceed to the next operation below by clicking [A] Yes button in the window. The correction factor FI accounts for the effect of the finite boundary, or the edge effect of the plate. The hybrid extrapolation method [1] is a blend of the two types of the extrapolation methods above and can bring about better solutions.

As illustrated in Figure 3. Table 3. The value of FI 0. The relative error of the present result is 1. Note that the quarter model described in the present section can be used for the FEM calculations of this problem simply by changing the boundary conditions. In this case, a half plate model which is clamped along the ligament and is loaded at the right end of the plate.

Note that the whole plate model with an edge crack needs a somewhat complicated procedure. Perform an FEM analysis of the elastic cylinder pressed against the elastic flat plate illustrated in Figure 3. Note that the cylinder and the plate is considered to have an unit thickness in the case of plane stress condition.

G [3] Combining the elastic cylinder and the flat plate models The elastic cylinder and the flat plate models Figure 3. Move this arrow to the quarter cylinder area and click this area, and then move the arrow on to the half plate area and click this area to combine these two areas.

Note that this element is defined as Type 1 element as indicated in the Element type reference number box. Select the Plane strain item in the Element behav- ior box and click the OK button to return to the Element Types window. In contact problems, two mating surfaces come into contact with each other exerting great force on each other. Contact elements must be used in contact problems for preventing penetration of one object into the other: 6 Repeat clicking the Add … button in the Element Types window to open the Library of Element Types window and select Contact and 2D target Note that this target element is defined as Type 2 element as indicated in the Element type reference number box.

Note that this target element is defined as Type 3 element as indicated in the Element type reference number box. The size Figure 3. It would be preferable that we may have smaller elements around the contact point where high stress concentration occurs. Finally, click [D] OK button to close the window. This section describes the elements of the Mechanical Application interface, their purpose and conditions, as well as the methods for their use. Currently, he is working in the sheet metal industry as a designer.

Additionally, he has interested in Product Design, Animation, and Project design. He also likes to write articles related to the mechanical engineering field and tries to motivate other mechanical engineering students by his innovative project ideas, design, models and videos.

Your email address will not be published. This self-contained, introductory text minimizes the need for additional reference material by covering both the fundamental topics in finite element methods and advanced topics concerning modeling and analysis. Extensive examples from a range of engineering disciplines are presented in a straightforward, step-by-step fashion.

Students, researchers, and practitioners alike will find this an essential guide to predicting and simulating the physical behavior of complex engineering systems. Additional topics covered include an introduction to commands, input files, batch processing, and other advanced features in ANSYS.

Exercises gradually increase in difficulty and complexity, helping readers quickly gain confidence to independently use the program.

This provides a solid foundation on which to build, preparing readers to become power users who can take advantage of everything the program has to offer. Written for students who want to use ANSYS software while learning the finite element method, this book is also suitable for designers and engineers before using the software to analyse realistic problems. The books presents the finite element formulations for solving engineering problems in the fields of solid mechanics, heat transfer, thermal stress and fluid flows.

For solid mechanics problems, the truss, beam, plane stress, plate, 3D solid elements are employed for structural, vibration, eigenvalues, buckling and failure analyses. For heat transfer problems, the steady-state and transient formulations for heat conduction, convection and radiation are presented and for fluid problems, both incompressible and compressible flows using fluent are analyzed. The book contains twelve chapters describing different analysis disciplines in engineering problems.

In each chapter, the governing differential equations and the finite element method are presented. An application example is also included at the end of each chapter to highlight the software capability for analysing practical problems. Providing an introduction to finite element modeling and analysis for those with no prior experience, and written by authors with a combined experience of 30 years teaching the subject, this text presents FEM formulations integrated with relevant hands-on applications using ANSYS Workbench for finite element analysis FEA.

Incorporating the basic theories of FEA and the use of ANSYS Workbench in the modeling and simulation of engineering problems, the book also establishes the FEM method as a powerful numerical tool in engineering design and analysis. The material in the book discusses one-dimensional bar and beam elements, two-dimensional plane stress and plane strain elements, plate and shell elements, and three-dimensional solid elements in the analyses of structural stresses, vibrations and dynamics, thermal responses, fluid flows, optimizations, and failures.

Contained in 12 chapters, the text introduces ANSYS Workbench through detailed examples and hands-on case studies, and includes homework problems and projects using ANSYS Workbench software that are provided at the end of each chapter. It will quickly become a welcome addition to any engineering library, equally useful to students and experienced engineers alike.

The finite element method FEM is indispensable in modeling and simulation in various engineering and physical systems, including structural analysis, stress, strain, fluid mechanics, heat transfer, dynamics, eigenproblems, design optimization, sound propagation, electromagnetics, and coupled field problems.

This textbook integrates basic theory with real-life, design-oriented problems using ANSYS, the most commonly used computational software in the field. For students as well as practicing engineers and designers, each chapter is highly illustrated and presented in a step-by-step manner.

Fundamental concepts are presented in detail with reference to easy to understand worked examples that clearly introduce the method before progressing to more advanced content. Included are step-by-step solutions for project type problems using modelling software, special chapters for modelling and the use of ANSYS and Workbench programs, and extensive sets of problems and projects round out each chapter. It essentially deals with the methods of calculation of the arc heat in a welded component when the analysis is simplified into either a cross sectional analysis or an in-plane analysis.

The book covers five different cases involving different welding processes, component geometry, size of the element and dissimilar material properties. Features: Provides useful background information on welding processes, thermal cycles and finite element method Presents calculation procedure for determining the arc heat input in a cross sectional analysis and an in-plane analysis Enables visualization of the arc heat in a FEM model for various positions of the arc Discusses analysis of advanced cases like dissimilar welding and circumferential welding Includes step by step procedure for running the analysis with typical input APDL program listing and output charts from ANSYS.

It covers simple text book problems, such as determining the natural frequencies of a duct, to progressively more complex problems that can only be solved using FEA software, such as acoustic absorption and fluid-structure-interaction. It also presents benchmark cases that can be used as starting points for analysis. Over the past two decades, the use of finite element method as a design tool has grown rapidly.

Easy to use commercial software, such as ANSYS, have become common tools in the hands of students as well as practicing engineers. The objective of this book is to demonstrate the use of one of the most commonly used Finite Element Analysis software, ANSYS, for linear static, dynamic, and thermal analysis through a series of tutorials and examples.