the finite element method a practical course

[...]... rectangular and quadrilateral elements are derived in detail Area and natural coordinates are also introduced in the process Iso-parametric formulation and higher order elements are also described An example of analysing a micro device is used to study the accuracy and convergence of triangular and quadrilateral elements Chapter 8: Deals with finite element matrices for plates and shells Matrices for rectangular... usually has a very simple geometry Figure 1.4 shows the finite element approximation for a one-dimensional 1 2 CHAPTER 1 COMPUTATIONAL MODELLING Conceptual design Modelling Physical, mathematical, computational, and operational, economical Simulation Experimental, analytical, and computational Analysis Photography, visual-tape, and computer graphics, visual reality Design Prototyping Testing Fabrication... commercial application software packages There are also packages designed mainly for meshing Such packages can generate files of a mesh, which can be read by other modelling and simulation packages Triangulation is the most flexible and well-established way in which to create meshes with triangular elements It can be made almost fully automated for two-dimensional (2D) planes, and even three-dimensional (3D)... wire-frames and deformations Usually, there are also tools available for the user to produce iso-surfaces, or vector fields of variable(s) Tools to enhance the visual effects are also available, such as shading, lighting and shrinking Animations and movies can also be produced to simulate the dynamic aspects of a problem Outputs in the form of tables, text files and x–y plots are also routinely available... materials are a special case of anisotropic material There are only two independent material constants for isotropic material Usually, the two most commonly used material constants are the Young’s modulus and the Poisson’s ratio This book deals mostly with isotropic materials Nevertheless, most of the formulations are also applicable to anisotropic materials Boundary conditions are another important... simplification required by the mathematical modelling For example, a plate has three dimensions geometrically The plate in the plate theory of mechanics is represented mathematically only in two dimensions (the reason for this will be elaborated in Chapter 2) Therefore, the geometry of a ‘mechanics’ plate is a two-dimensional flat surface Plate elements will be used in meshing these surfaces A similar situation... in a rapid and cost effective way So what is the FEM? The FEM was first used to solve problems of stress analysis, and has since been applied to many other problems like thermal analysis, fluid flow analysis, piezoelectric analysis, and many others Basically, the analyst seeks to determine the distribution of some field variable like the displacement in stress analysis, the temperature or heat flux in thermal... three-dimensional (3D) spaces Therefore, it is commonly available in most of the pre-processors The additional advantage of using triangles is the flexibility of modelling complex geometry and its boundaries The disadvantage is that the accuracy of the simulation results based on triangular elements is often lower than that obtained using quadrilateral elements Quadrilateral element meshes, however, are more difficulty... thermal analysis, the electrical charge in electrical analysis, and so on The FEM is a numerical method seeking an approximated solution of the distribution of field variables in the problem domain that is difficult to obtain analytically It is done by dividing the problem domain into several elements, as shown in Figures 1.2 and 1.3 Known physical laws are then applied to each small element, each of... matrices for truss and beam elements Details on obtaining the transformation matrix and the transformation of matrices between the local and global coordinate systems are described An example is given to demonstrate the use of frame elements to solve practical engineering problems Chapter 7: Formulates the finite element matrices for 2D solids Matrices for linear triangular elements, bilinear rectangular . practical problems and structural analysis and heat transfer. Important fundamental and classical theories are introduced in a straightforward and easy to understand fashion. Modern, state-of -the- art. COMPUTATIONAL MODELLING Modelling Physical, mathematical, computational, and operational, economical Simulation Experimental, analytical, and computational Analysis Photography, visual-tape, and. problems. Chapter 7: Formulates the finite element matrices for 2D solids. Matrices for linear triangular elements, bilinear rectangular and quadrilateral elements are derived in detail. Area and natural