Engineering

## A Primer On Finite Element Analysis

Now-a-days FEM has become a common tool for solving Engineering problems in industries for the obvious reasons of its versatility and affordability. To expose an UG student to this powerful method most of the universities have included this subject in the UG curriculum. There are many good books on the subject available in the market. This book contains complementary/supplementary material to the textbooks covering comprehensively the theoretical aspects of the subject. This book is written primarily to help the students as a gentle introduction to the practice of FEM. This book contains many 1-D and 2-D problems solved by analytical method, by FEM using hand calculations and by using commercial FEM, ANSYS 12 academic teaching software. Results of all the methods have been compared. This helps the students in building confidence in the method. Chapter 1 contains brief introduction to FEA, theoretical background and its application. Chapter 2 contains the linear static analysis of bars of constant cross-section, tapered cross-section and stepped bar. In each section different variety of exercise problems are given. Chapter 3 contains the linear static analysis of trusses. Trusses problems are also selected in such way that each problem is having different boundary conditions to apply. Chapter 4 contains the linear static analysis of simply supported and cantilever beams. In the chapters 2 to 4 all the problems are considered as one dimensional in nature. Stress analysis of rectangular plate with a circular hole is covered in chapter 5. In this chapter emphasis is given on the concept of exploiting symmetric geometry and symmetric loading conditions. Also stress and deformation plots are given. Chapter 6 contains the thermal analysis of cylinders and plates. Here both one dimensional and two dimensional problems are considered. Chapter 7 contains the problems of potential flow distribution over a cylinder and over an airfoil. Chapter 8 contains the dynamic analysis (modal and transient analysis) of bars and beams. Chapter 9 contains the introduction to ANSYS Workbench.
• Publisher: Laxmi Publications
• Language: English
• ISBN : 978-93-81159-10-1
Total Price: 26.91
• Chapter 1

### INTRODUCTION TO FINITE ELEMENT ANALYSIS Price 2.99  |  2.99 Rewards Points

There are three methods to solve any engineering problem: 1. Analytical method, 2. Numerical method, 3. Experimental method.
• Chapter 2

### FINITE ELEMENT ANALYSIS OF AXIALLY LOADED MEMBERS Price 2.99  |  2.99 Rewards Points

Bar Element is used in the analysis of rod-like axially loaded members. There are two popular bar elements.
• Chapter 3

### FINITE ELEMENT ANALYSIS OF TRUSSES Price 2.99  |  2.99 Rewards Points

Truss by definition, is a load bearing structure formed by connecting members using pin joints. Truss element is used in the analysis of 2-D trusses.
• Chapter 4

### FINITE ELEMENT ANALYSIS OF BEAMS Price 2.99  |  2.99 Rewards Points

Beam by definition is a transversely loaded structural member. Beam element is used in the analysis of beams. This element has two end nodes each having two degrees of freedom, namely transverse displacement and slope. Beam element gives accurate results if acted upon by nodal forces and moments. More number of small elements will be necessary in the case of a beam acted upon by distributed loads in order to get good results. The interpolation equation and element stiffness matrix for beam element are given by
• Chapter 5

### STRESS ANALYSIS OF A RECTANGULAR PLATE WITH A CIRCULAR HOLE Price 2.99  |  2.99 Rewards Points

Two dimensional problems in structural analysis are dealt in this chapter. Hand calculations, even with two elements, become too long and hence are not given for these problems; only analytical method solutions and software solutions have been provided. Two dimensional problems can either be plane stress or plain strain problems. Method of analysis is same for both, except that stress strain matrix is different in two cases. Plane bodies that are flat and of constant thickness subjected to in-plane loading fall under the category of plane stress problems. Stress components z, xz and yz assume zero values in these problems. Some of the elements used in the analysis of two dimensional problems are constant strain triangle(CST), linear strain triangle(LST), linear quadrilateral, isoparametric quadrilateral, etc. each of these elements has two degrees of freedom per node namely translation in x and y directions. Stress within the element may be calculated using the equation, {} = [D][B]{q} The stress analysis of a rectangular plate with a circular hole problem is assumed as a two dimensional plane stress problem. Plane stress is defined to be a state of stress in which the normal stress and the shear stress directed perpendicular to the plane are assumed to be negligible. The above problem can be categorized into 3 sub cases. Sub Case 1 A rectangular plate with a very small circular hole at the centre with one vertical edge fixed and the other vertical edge is acted upon by a horizontal tensile load in the form of pressure.
• Chapter 6

### THERMAL ANALYSIS Price 2.99  |  2.99 Rewards Points

Thermal analysis is one of scalar field problems. These problems have only one degree of freedom per node namely temperature. In this chapter, one-dimensional and two-dimensional heat conduction problems are dealt with. In these problems bar element with two end nodes each having temperature (T) as sole degree of freedom is made use of. Nodal heat flow rates (Q) or heat fluxes are analogous quantities to nodal forces, in structural bar element.
• Chapter 7

### FLUID FLOW ANALYSIS Price 2.99  |  2.99 Rewards Points

This chapter covers the finite element solution of ideal or potential flow (inviscid, incompressible flow) problems. Typical examples of potential flow are flow over a cylinder, flow around an airfoil and flow out of an orifice. The two-dimensional potential flow (irrotational flow) problems can be formulated in terms of a velocity potential function () or a stream function (). The selection between velocity and stream function formulations in the finite element analysis depends on the ease of applying boundary conditions. If the geometry is simple any one function can be used.
• Chapter 8

### DYNAMIC ANALYSIS Price 2.99  |  2.99 Rewards Points

Structural dynamics encompasses modal analysis, harmonic response analysis and transient response analysis. Modal analysis consists of finding natural frequencies and corresponding modal shapes of structures. Finding amplitude of vibration when the loads vary sinusoidal with time is known as harmonic response analysis. Finding the structural response to arbitrary time dependent loading is referred to as transient response analysis.
• Chapter 9

### ANSYS WORKBENCH Price 2.99  |  2.99 Rewards Points

ANSYS workbench provides unified data sharing and project file management across the range of ANSYS products. Workbench is not an application on its own. It is a group of technologies for developing simulating tools. This has been created by ANSYS incorporation to help developers to develop robust tools to meet the needs of designers and analysts. It provides a common interface for the user to access the wealth of technology that ANSYS has with it. Simulation data is displayed in a hierarchical tree that separates out the various groups of inputs and outputs. Workbench makes use of a Project file storage method to assist with the organization of data, and each can contain all types of information.