A Consistent Formulation of Trusses and Non-Warping Beams in Linearized Finite Displacements

Liyanage

Nishino

1987

Self Cite

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.

“…The tangent stiffness equation for non-warping members is found in Ref. 12. The crest of the structure is allowed for the displacements in the vertical direction only.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The stiffness equation for trusses is found in Ref. 12. The load-displacement behaviour for the truss idealization (all joints are assumed to be hinged, instead of the rigid joint condition assumed in frame analysis) of the twelve member hexagonal frames considered previously is obtained, as shown in Fig.…”

Section: Numerical Examplesmentioning

confidence: 99%

A Non-Iterative Nonlinear Analysis Scheme of Frames With Thin-Walled Elastic Members

Liyanage

Nishino

1987

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“…The additional matrices Ka, Kb and Fo which have not appeared in Refs. 10), 12) can be incorporated into the nonlinear analysis scheme for elastic thin-walled frames and beamsll.…”

Section: Finite Element Modelmentioning

confidence: 99%

Effects of Load Point Location on the Instability and Nonlinear Behaviour of I, Channel, and Zee Shaped Beams

Anwar²,

Teshome

1989

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The effects due to an arbitrary location of the load point on the buckling and post-buckling behaviour of elastic thin-walled beams are investigated. The governing differential equations and the corresponding stiffness matrices are derived, based on the virtual work equation of linearized finite displacement. Numerical examples are given to investigate the behaviour of I, channel and zee shaped beams. Location of load point greatly affects the post-buckling behaviour as well as the buckling loads. Although zee and channel sections show a large reserve strength as compared with I-section, this reserve strength corresponds to fairly large stresses and displacements.

“…The hinge at the loaded point is inserted by the technique described in Ref. 19). Since the component members are relatively slender, there exists one bifurcation point before this structure shows the snap-through phenomenon at B, although a "truss" with the same geometry does not show such a bifurcation because of its rather small rise H without bending freedom20).…”

Section: Stability Of Simple Structuresmentioning

confidence: 99%

Principle and Numerical Check of a Stiffness Equation for Plane Frames

Iwakuma

Nishino

et al. 1987

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A stiffness equation of plane frames is formulated in finite displacements by the total Lagrangian approach. The formulation is based on the physical interpretation of the polar decomposition theorem and does not use any variational principle. The corresponding differential equations are also given to show which theoretical solutions the discretized ones converge to. For the Bernoulli-Euler beam, the postbuckling behavior can be analysed accurately without the geometric stiffness matrix which helps to accelerate the convergence of solutions. On the other hand, the Timoshenko beam element must have the geometric stiffness in order to obtain the correct solutions. Finally the typical stability problems which have the bifurcation points in their equilibrium paths are solved to demonstrate the ability of the stiffness equation.