Showing papers on "Tangent stiffness matrix published in 1985"

A note on tangent stiffness for fully nonlinear contact problems

Abstract: SUMMARY In the numerical solution of geometrically nonlinear contact problems by the finite element method, it is often assumed that the modification to the tangent stiffness takes the form of the single rank-one-update characteristic of the linear theory. It is shown that due to the kinematic nonlinearity such a simple structure no longer holds. Within the context of the discrete problem arising from a finite element formulation, explicit expressions for the residual and the tangent stiffness matrix are obtained for both penalty and Lagrangian parameter procedures. FORMULATION OF THE DISCRETE PROBLEM By introducing the perturbed Lagrangian functional, both penalty and Lagrange parameter procedures may be presented in a unified manner. For the discrete description of the contact problem, the perturbed Lagrangian function, re, may be expressed as

Postbuckling analysis using a general purpose code

Abstract: A new capability for solving postbuckling problems in shell structures is described. The matrix theory to adapt Newton's method to nonlinear finite element shell analysis is outlined first. The matrix theory is directed at writing consistent linear algebratic equations for problems where the tangent stiffness matrix is singular or nearly singular. The matrix theory suggests a change of variables as part of the usual iterative procedure in Newton's method. The change of variables is shown to be feasible for introduction into the algorithm programmed in general purpose codes for finite element analysis of structures. Numerical results from a new option that has been programmed in an existing general purpose code are presented. The analysis of shell structures for collapse and for branching at bifurcation loads is illustrated by the numerical examples.

A simple approach to bifurcation and limit point calculations

Abstract: A simple approach is proposed to calculate the bifurcation and limit points of structures, talcing into account the pre-unstable behaviour, by the finite element method. The approach is as follows: at each load step, the triangular factorization of the tangent stiffness matrix is checked to determine if the matrix is positive definite or not. When the tangent stiffness matrix is positive definite at a certain load step and non-positive definite at the next load step, the structure is considered to become unstable between the two load steps and an eigenproblem is constructed based on the difference of the tangent stiffness matrices at the two load steps. The critical load and corresponding mode of the structure are then derived from solving the eigenproblem. The proposed procedure is simple and economical, and it can be easily incorporated into a conventional geometric nonlinear analysis computer program. It is implemented in the ADINA program and some sample calculations are shown.

Simplified Nonlinear Analysis of Large Space-Trusses and Space-Frames, Using Explicitly Derived Tangent Stiffnesses and Accounting for Local Buckling.

Abstract: : Simplified finite element methods for finite deformation, post-buckling analysis of large space trusses and space frames are presented Arbitrarily large rigid translations and rigid rotations of each member are accounted for Each 3-D truss member is assumed to withstand an axial force, while each 3-D frame member is assumed to withstand two bending moments, a twisting moment, and transverse and axial forces at each node The influence of local (member) buckling on global instability is systematically examined For both 3-D truss and frame members, explicit tangent stiffness matrices are derived By 'explicit;' it is meant that no element-wise basis functions are assumed and that no element-wise numerical integrations are involved These explicit tangent stiffness matrices are very simply evaluated at any point in the load deformation history of a space truss, or space frame, undergoing large deformations, as well as in the post-buckled region of behavior of these structures An arc-length method is implemented to trace the post-buckling behavior of these large space structures A large number of examples are included to: (1) bring out the economy as well as accuracy of the simplified method developed; (2) indicate the effectiveness of the present method in creating reduced-order models of large space structures; and (3) delineate the process whereby the overall behavior of the structure can be vastly improved by controlling the deformation of individual members through active or passive mechanisms Keywords: Reduced order model; Simplified nonlinear analysis; Finite deformations; Finite rotations; Semi-tangential rotations; Exact tangent stiffness matrix; LSS (Large Space Structure) control; Arc-length method

The condensation of the boundary element stiffness matrix in FEBEM analysis

Abstract: Two alternatives are discussed to take into consideration symmetry due to shape and loading in the development of the boundary element stiffness matrix. The resulting boundary element stiffness matrix is coupled with the finite element stiffness matrix and the displacements are computed for a circular tunnel. There is a considerable saving in computation time when symmetry is considered by either of the alternatives, but one appears to be preferable to the other.

Condensation of elastic half space soil stiffness matrix considering symmetry

Abstract: The finite element formulation for deriving the soil stiffness matrix by idealizing the foundation as an elastic half space is presented. The procedure for condensation of the soil stiffness matrix taking symmetry into consideration is discussed. Computation time is considerable reduced when a condensed soil stiffness matrix is used for the finite element analysis of rafts resting on an elastic half space.