Showing papers on "Tangent stiffness matrix published in 1987"

Large-deformation, elasto-plastic analysis of frames under nonconservative loading, using explicitly derived tangent stiffnesses based on assumed stresses

Abstract: Simple and economical procedures for large-deformation elasto-plastic analysis of frames, whose members can be characterized as beams, are presented. An assumed stress approach is employed to derive the tangent stiffness of the beam, subjected in general to non-conservative type distributed loading. The beam is assumed to undergo arbitrarily large rigid rotations but small axial stretch and relative (non-rigid) point-wise rotations. It is shown that if a plastic-hinge method (with allowance being made for the formation of the hinge at an arbitrary location or locations along the beam) is employed, the tangent stiffness matrix may be derived in an explicit fashion, without numerical integration. Several examples are given to illustrate the relative economy and efficiency of the method in solving large-deformation elasto-plastic problems. The method is of considerable utility in analysing off-shore structures and large structures that are likely to be deployed in outerspace.

A non-iterative nonlinear analysis scheme of frames with thin-walled elastic members

Abstract: The purpose of this study is to establish a non-iterative efficient computational scheme to trace the nonlinear finite displacement behaviour of space frames, using the tangent stiffness equation of linearized fininte displacement of a thin-walled elastic straight beam element. Direct solution of the tangent stiffness equation is used, imposing adequately small increments. Local coordinates are updated at each incremental step, utilizing a vector multiplication scheme. Numerical results for a wide variety of spatial structures are given, demonstrating the versatility of the present scheme.

Effects of Three-Dimensionality and Nonlinearity on the Dynamic and Seismic Behavior of Cable-Stayed Bridges

Abstract: The cases of multiple-support as well as uniform seismic excitations of these long and flexible structures are considered; furthermore, effects of the nondispersive travelling, seismic-wave on the bridge response are studied. Different sources of nonlinearity for such bridges are included in the analysis using the large deflection theory. A tangent stiffness iterative procedure is utilized in the analysis to capture the nonlinear seismic response. Numerical examples are presented in which a comparison between a linear earthquake-response analysis (based on the utilization of the tangent stiffness matrix of the bridge at the dead-load deformed state which is obtained from the geometry of the bridge under gravity load conditions), and a nonlinear earthquake-response analysis using the step-by-step integration procedure is made. In these examples, two models having center (or effective) spans of 1100 ft (335. 5m) and of 2200 ft (671 m) are studied; this range covers both present and future designs.

An inelastic finite displacement formulation of thin-walled members

Abstract: The stiffness equation of linearized finite displacements for straight thin-walled members with inelastic material is derived. An arbitrary orthogonal coordinate system with a single reference point across the section need be introduced in the formulation, which is a clear distinction from the elasticity problem. Also distinct from the elastic analysis is a need to evaluate the magnitude of strains from time to time because of the dependence of the tangent modulus on strain levels. Illustrative examples are given to demonstrate the proposed method for the inelastic finite displacement analysis of spatial thin-walled members, with a simplified consideration on the effect of shear stresses.

Nonlinear analysis of structures composed of thin-walled beam-columns

Abstract: The linear and geometric stiffness matrices for a general thin-walled beam-column are formulated, incorporating the important second order terms in the governing energy equation. The derived stiffness matrices are then used to predict the bifurcation loads of various structures. The effects of eccentric connections and inclined principal planes have also been included in the formulation of the tangent stiffness matrix and in the secant stiffness relationship. An updated Lagrangian formulation, coupled with the numerical arc-length technique, is employed to trace the geometric nonlinear pre- and post- buckling equilibrium paths of different structures. Based on a simplified material model allowing for the effects of strain-unloading, the procedure is further extended to the elasto-plastic large deflection analysis of framed structures. Numerous examples have been employed to validate the theory and the numerical procedure.

Geometric and material nonlinear analysis of structures comprising rectangular hollow sections.

Abstract: This paper presents a nonlinear finite element analysis of structures comprising thin-walled rectangular hollow sections. Nonlinearities due to both the change of geometry and material yielding are included, incorporataing also the effects of strain-unloading. The geometry and the stiffness of the elements are modified and used to update the structure tangent stiffness matrix. An iterative procedure combining the arc-length and the work methods is employed for the solution of the incremental equation of equilibrium. The method has been applied successfully to predict the nonlinear load-deflection behavior of isolated cold-formed SHS columns, fabricated RHS parabolic fixed end arches, and double chord SHS trusses having different joint configurations.