[...]... market A semi-automatic pre-processor is available for most 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... 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 and quadrilateral elements are derived in detail Area and natural coordinates are also introduced in the process Iso-parametric formulation and higher order elements... 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 plate elements based on the more practical Reissner–Mindlin plate theory are derived in detail Shell elements are formulated simply by combining the plate elements... 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 analysis, the electrical... and heat transfer The aim of the book is to provide the necessary concepts, theories and techniques of the FEM for readers to be able to use a commercial FEM package comfortably to solve 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 treatment of engineering... two-dimensional (2D) planes, and even 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... 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... 1.4 shows the finite element approximation for a one-dimensional 1 “chap01” — 2002/12/14 — page 1 — #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 Figure... understanding of the fundamentals and principles of linear FE analysis We have chosen ABAQUS as it can easily handle linear analyses, however, with further reading readers could also extend the use of ABAQUS for projects involving non-linear FE analyses too Preparing lectures for FEM courses is a very time consuming task, as many drawings and pictures are required to explain all these theories, concepts and techniques... essential (displacement) condition is satisfied, the process will lead to the equilibrium equations as well as the force boundary conditions This means that the force boundary condition is naturally derived from the process, and it is therefore called the natural boundary condition Since the terms essential and natural boundary do not describe the physical meaning of the problem, it is actually a mathematical . 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