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Showing papers on "Tangent stiffness matrix published in 1984"


Journal ArticleDOI
TL;DR: In this paper, an approximate method for the analysis of elastoplastic plane frames in the presence of finite displacements is presented, where the nonlinear tangent stiffness matrix is taken into account.

8 citations


Journal ArticleDOI
TL;DR: In this article, a nonlinear finite element computer program was developed to analyze thin-walled metal structural members, which has the ability to handle both geometrical and material nonlinearities so that the postbuckling behaviour and ultimate strength of members can be predicted.
Abstract: A nonlinear finite element computer program has been developed to analyse thin-walled metal structural members. The program has the ability to handle both geometrical and material nonlinearities so that the post-buckling behaviour and ultimate strength of members can be predicted. A bending-membrane rectangular element with six degrees of freedom at each node forms the basic type of element used in the program. Marguerre's shallow shell theory is adopted for the strain-displacement relationships and hence the bifurcation point at buckling can be bypassed by providing an initial inperfection. The finite element formulation is based on the total Lagrange coordinate system and the flow theory of plasticity. Explicitly shown in the paper is the formation of the tangent stiffness matrix and the tridiagonal block form of solution procedure. Two problems of a square tube and a channel section beam subjected to pure bending were tested and found to be in close agreement with previous theoretical work.

7 citations


01 Feb 1984
TL;DR: In this paper, the joint area between beam type elements may be regarded as a sub-structure, the behaviour of which may be defined by the stiffness or flexibility matrix, and the method of inputting the derived stiffness matrix into the PAFEC 75 finite element program is fully described with examples.
Abstract: The joint area between beam type elements may be regarded as a sub-structure, the behaviour of which may be defined by the stiffness or flexibility matrix. The flexibility of such a sub-structure may be determined experimentally by the measurement of displacements under a variety of loading conditions, and the report describes the method of obtaining the stiffness matrix from this data. Alternatively, the joint area may be analysed by a detailed finite element calculation and the report describes two methods of obtaining the stiffness matrix, one using applied forces, the other by prescribing displacements. The method of inputting the derived stiffness matrix into the PAFEC 75 finite element program is fully described with examples. (Author/TRRL)

1 citations


Book ChapterDOI
01 Jan 1984
TL;DR: The present chapter contains a general approach to the construction of algorithms for optimum problems, both static and dynamic, looking for constrained extrema of functions or functionals by means of solving unconstrained problems.
Abstract: The present chapter contains a general approach to the construction of algorithms for optimum problems, both static and dynamic. The reader will certainly notice a resemblance to the classical Newton method (tangent method), but there is an essential difference: we are looking for constrained extrema of functions or functionals by means of solving unconstrained problems. The functions involved are well-known mathematical objects and they play an important role in dynamic programming [21]. Again we shall pay a lot of attention to significant mechanical analogies.

1 citations