Showing papers on "Tangent stiffness matrix published in 1972"
TL;DR: In this article, a method for computing generalized stress-strain relationships (moment-thrustcurvature relationships) for metal column sections in biaxial bending is described.
Abstract: A method for computing generalized stress-strain relationships (moment-thrust-curvature relationships) for metal column sections in biaxial bending is described. The analytical formulation of the force-deformation equations in terms of the rate of change leads to a linear relationship between these quantities. Solutions are obtained by the tangent stiffness method and a digital computer. The method is found to be extremely powerful and efficient for computer solution.
29 citations
TL;DR: In this article, the authors derived expressions for the pseudo forces and contributions to the tangent stiffness matrix for geometric and material nonlinearities using the basic principle of virtual work and a computional procedure is presented which evaluates the effects of non-linearities through the use of finite difference expressions.
20 citations
01 May 1972
TL;DR: A DISCRETE ELEMENT ANALYSIS as discussed by the authors, which is based on an ITERATIVE PROCEDURE called the TANGENT STIFFness METHOD, is used to evaluate the performance of a general discemble.
Abstract: A DISCRETE ELEMENT ANALYSIS WHICH CONSIDERS GEOMETRIC, MATERIAL, AND SUPPORT NONLINEARITIES OF STATICALLY LOADED PLANE FRAMES IS DEVELOPED. A COMPUTER PROGRAM HAS BEEN WRITTEN TO IMPLEMENT AND VERIFY THE ANALYSIS. FRAME GEOMETRY, LOADS, CROSS SECTIONS, AND SUPPORTS (NONLINEAR CONCENTRATED AND DISTRIBUTED SPRINGS) CAN BE SUFFICIENTLY GENERAL TO WORK PRACTICAL FRAME PROBLEMS. THE METHOD OF ANALYSIS IS BASED ON AN ITERATIVE PROCEDURE CALLED THE TANGENT STIFFNESS METHOD. UNBALANCED NODAL POINT FORCES ARE APPLIED TO A TEMPORARILY LINEAR STRUCTURE WHOSE POSITION DEPENDENT STIFFNESS MATRIX IS THE TANGENT STIFFNESS MATRIX OF THE STRUCTURE. THE FRAME MEMBERS ARE DIVIDED INTO A NUMBER OF DISCRETE ELEMENTS. LOAD-DISPLACEMENT EQUATIONS FOR AN INDIVIDUAL DISCRETE ELEMENT ARE DERIVED WHICH ARE VALID FOR LARGE DISPLACEMENTS. A NUMERICAL TECHNIQUE IS USED TO DETERMINE THE FORCE-DEFORMATION RESPONSE OF A CROSS SECTION WITH NONLINEAR STRESS-STRAIN CURVES. LOADS AND NONLINEAR SUPPORTS ARE INPUT IN NORMAL ENGINEERING TERMS AND CAN BE REFERENCED EITHER TO THE STRUCTURE OR TO THE MEMBER AXES. WHEN NECESSARY, THE LOADS AND NONLINEAR SUPPORTS ARE INTERNALLY TRANSFORMED TO MEMBER COORDINTES AND DISCRETIZED TO CONCENTRATED VALUES AT THE NODAL POINTS. CASTIGLIANO'S FIRST THEOREM IS APPLIED TO DEVELOP MATRIX EXPRESSIONS FOR THE STIFFNESS MATRIX OF A GENERAL DISCRETE ELEMENT AND THESE EXPRESSIONS ARE USED TO OBTAIN THE STIFFNESS MATRIX FOR THE SPECIFIC DISCRETE ELEMENT USED IN THE FRAME SOLUTIONS. A NUMBER OF PROBLEMS ARE WORKED AND COMPARED WITH EXISTING ANALYTICAL OR EXPERIMENTAL SOLUTIONS.
1 citations
10 Apr 1972
TL;DR: In this article, a derivation of finite element equations of and solution to the viscoelastoplastic response of an isotropic axisymmetric shell is presented.
Abstract: A derivation of finite element equations of and solution to the viscoelastoplastic response of an isotropic axisymmetric shell are presented herein. The generalized Maxwell model is incorporated into the von Mises isotropic yield function. This permits a derivation of the incremental stress as a function of elastic, viscous, and plastic strains. With this relationship inserted into the incremental equation of motion, a direct numerical integration scheme is then used to solve for incremental responses. The plastic tangent stiffness matrix is updated at each incremental time step. Numerical results are presented for a circular plate to verify correctness of the program and subsequently for a spherical cap subjected to uniformly distributed transverse impulsive load of infinite duration.