This book uses fundamental theorems of structural mechanics to explain the connection between statics of structures and their deflections on the one hand, and the kinematics of structures and their equilibrium on the other. It develops the theory and techniques of finite element and non-linear analysis applicabale to computer software. Computer Methods in Structural Analysis brings a unified approach to the analysis of conventional truss and frame structures and the finite element approximation of the continuum via the priciples of virtual displacements and virtual forces. These principles can be succintly expressed in the form known as the contragredient law. Concepts of elasticity and elasto-plastic constitutive laws are discussed and a broad introduction given to the various approaches used in the finite element method. A treatment is then given for line element structures using both the force and the displacement method, and in the latter case, the theory is extended for non-linear large displacement analysis. Practical means are presented for the calculation of critical loads on such structures.
Three chapters are devoted to the finite element method in which continuum thoery, torsion, heat transfer, plates and shells are discussed in some detail. In this finite element theory, both conventional methods (via contragredience) and the natural mode technique of Processor J H Argyris are explained. Topics such as the calculation of the shear centre via the finite element method are also included. Various plate elements are discussed in detail and studies of their performance, and the new DKL facet element are presented. Tension net and tension fabric structures and thier shape determination and analysis are comprehensively discussed. Details are given for eliminating the shear and membrane locking experienced in the simple formulation of the isoparametric degenerate shell element.
Part 1 Mathematical preliminaries: notation vector, matrix, index; the Gauss divergence theorem; interpolation. Part 2 Basis of solid mechanics - fundamental theorems: strain; stress; the inertia tensor - inertia matrix; stress equilibrium; application of Gauss' divergence theorem; the contragredient principle; discrete force and displacement systems; the constitutive relationships; theories of failure; examples of yield surfaces; temperature and creep effects. Part 3 The formulation of the finite element method: displacement formulation; the natural mode technique; the method of weighted residuals; hybrid element formulation; equilibrium elements; convergence of finite element solutions. Part 4 The force method - line element structure: line elements - member forces; calculation of deflections; effects on members; statically indeterminate structures; algorithms suitable for computer analysis; deflections of curved members; member flexibility matrices; deflection along member; non-linear structure behaviour; analysis of planar cable structure. Part 5 The displacement method - line element structures: structure stiffness; initial strains - modification of member stiffness; member stiffness matrices; the direct stiffness method; condensation of stiffness matrices; the direct stiffness method; special element stiffness matrices. Part 6 The direct stiffness method - non-linear analysis: tension structures; practical shape finding of cable nets; calculation of elastic critical loads; geometric stiffness for thin-walled open sections; practical evaluation of eigenvalues and eigenvectors; non-linear transformation matrices; large displacement analysis of frame structures. Part 7 The solid continuum: plane elasticity; the triangle element family-straight sides; generalized (kinematically equivalent) force systems; torsion of prismatic shafts; the three dimensional solid; heat transfer-finite element approximation. Part 8 Plate bending: introduction to plate theory; the finite element formulation; quadrilateral plate bending elements; some comparative studies on plate bending elements. Part 9 Shells: membrane analysis of shells; membrane and bending shell elements; isoparametric degenerated three dimensional shell elements.
Number Of Pages: 524
Published: 8th August 1991
Country of Publication: GB
Dimensions (cm): 24.61 x 18.9
Weight (kg): 0.93
Edition Number: 1