Geometrically nonlinear analysis of space frames by an incremental iterative technique

Post-buckling analysis of spatial structures by vector iteration methods

Hypermatrix solution of large sets of symmetric positive-definite linear equations

Publisher Summary This chapter aims at presenting fundamental concepts for the implementation of the finite-element method, with primary emphasis on static analysis based upon the displacement method. The correct interpretation of information feedback from the user's side in the course of the development of a large-scale system should have a significant effect upon its applicability. Thus the ideal developers of computer software for the application of finite element methods would be design engineers with several years of experience in the development of large computer systems and with some basic understanding of numerical analysis. The internal data are handled in the internal machine representation, thus excluding transferability between computers with different word length. All internal data handling can be concentrated in a separate data retrieval package with sufficient parametric generality to enable its adaptation to a large spectrum of computer configurations. The solution of the linear load-deflection equations is usually the most time-consuming computation step in the displacement method. As the finite-element method is ideally suited for analyzing highly complex structures, problems with several thousand unknowns occur frequently.

Computer Implementation of the Finite-Element Procedure

Stability of trusses under dynamic loads

A comprehensive compilation of the stiffness method is presented for the general analysis of plane and space structures At first, the stiffness matrices of members with uniform cross-sections are derived relative to both the member and common axes, for various end deformation conditions ranging from a plane truss to a space frame member The member stiffness matrices are suitably modified to include the effects of variable moment of inertia, shear deformations, wide supports and semirigid connections The solution technique for large-size band matrices with multiple load vectors is presented and some computer programming for important phases of the analysis is introduced The classification of structures with one or two dimensional members, is examined Numerical examples for space frames are also included

Computer Analysis of Plane and Space Structures

This presentation is concerned with the derivation of a 12 by 12 tangent stiffness matrix for a space frame member with constant cross-section. At first, the member end forces are expressed in the coordinate axes of the deformed geometry of the member in terms of the total end displacements. Then, in accordance with the Taylor expansion method, the stiffness influence coefficients are obtained as the partial derivatives of the force vector with respect to each one of the twelve member end displacements. It is believed that when this tangent stiffness matrix is used in connection with the Newton-Raphson iteration scheme in analyzing geometrically nonlinear structures, both the speed of convergence and the accuracy of the results are substantially increased. Numerical results are included to demonstrate the efficiency of the tangent stiffness matrix presented.

Semih S. Tezcan

Papers

Computer Analysis of Plane and Space Structures

Tangent Stiffness Matrix for Space Frame Members

Discussion of “Simplified Formulation of Stiffness Matrices”

Discussion of Numerical Solution of Nonlinear Structures by Trevor J. Poskitt

Nonlinear analysis of thin plates by framework method.