The finite element method in engineering
This second edition of The Finite Element Method in Engineering reflects the new and current developments in this area, whilst maintaining the format of the first edition. It provides an introduction and exploration into the various aspects of the finite element method (FEM) as applied to the solution of problems in engineering. The first chapter provides a general overview of FEM, giving the historical background, a description of FEM and a comparison of FEM with other problem solving methods. The following chapters provide details on the procedure for deriving and solving FEM equations and the application of FEM to various areas of engineering, including solid and structural mechanics, heat transfer and fluid mechanics. By commencing each chapter with an introduction and finishing with a set of problems, the author provides an invaluable aid to explaining and understanding FEM, for both the student and the practising engineer.
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INTRODUCTION TO FINITE ELEMENT METHOD
SOLUTION OF FINITE ELEMENT EQUATIONS
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application array assumed axes beam body boundary conditions characteristic matrix components computed considered constant corresponding degrees of freedom denotes derived differential equation dimensional eigenvalue problem eigenvectors element characteristic equilibrium equations evaluated expressed field variable finite element analysis finite element equations finite element method flow fluid forces Galerkin method given by Eq heat transfer hence integral International Journal interpolation functions interpolation model interpolation polynomials iteration Jacobi method Journal for Numerical linear load vector mass matrix mechanics Methods in Engineering mode shapes natural coordinates natural frequencies nodal degrees nodal displacements nodal unknowns nodal values node node number Numerical Methods obtain one-dimensional plane plate procedure quadratic satisfied shape functions shown in Fig solid mechanics solution of Eq solving Step stiffness matrix strain stream function stress structure subroutine surface tetrahedron three-dimensional total number triangular element variation vector of nodal velocity Young's modulus zero