Mechanics in Geometrically Nonlinear Problem of Discrete System and Application to Plane Frame-Works

Nakano³

1997

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In the global buckling of a framed structure, members are examined for their own stabilities. It is shown that, besides the actual member forces exerted, there can be considered a critical axial force of each member determined by its displacement mode in the global buckling. The effective lengths of members are defined for those critical forces. The stability state of each member is qualified by the actual axial force acting on that effective length. The global buckling is explained as an assembly of those stability states of members.

Section: Discussionmentioning

confidence: 86%

Section: Numerical Analysismentioning

confidence: 99%

See 1 more Smart Citation

On the Stability of Frame Members in a Global Buckling

Nakano³

1997

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“…In the Cartesian {x, y}, let us consider a threenode triangular element (e). The spatial coordinates of its three nodes are employed as the element position {x} (e)={(x, y) i, (x, y), (x, y) k} (1) where i < j < k. As the element coordinate system, we take {x', y'} in relation to the current configuration such that x' is directed from node i toward j with y' being perpendicular to x'. As well, in the initial (or stress-free) state, the {x', y'} of material points are employed as Lagrangian coordinates {S ri}:S=xo, ij=yo, where an initial quantity is denoted by subscript ()o.…”

Section: Description Of Geometry and Strainmentioning

confidence: 99%

“…In this paper, another formulation is presented for the 2-D triangular element, with a full physical explanation, which is developed explicitly in a complete accordance with an exisiting general procedure stated in Ref. 1,2) to separate the total freedom of an element into the parameters of position as a rigid and those of deformation. By the assumption of an elastic strain energy existing even for finite strains, the realistic material problems are disregarded, but the expansion classified into the total-Lagrangian is theoretical and rigorous as a geometrically nonlinear discretization.…”

Section: Introductionmentioning

confidence: 99%

An Explicit Fem Formulation of the 2-D Triangular Element for Finite Strains

1992

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Not by means of mathematical expansions, but on the basis of a physical decomposition of its total freedom into the parameters of position as a rigid and those of deformation, an explicit discretization is developed for the 2-D triangular element with large displacements. While the material is assumed elastic even for finite strains, any geometrically nonlinear effects are taken into account, systematically and rigorously.

Accuracy and Convergence of the Separation of Rigid Body Displacements for Plane Curved Frames

Gotō

Hasegawa

1984

The method with the separation of rigid body displacements is a powerful tool for the finite displacement analysis of structures particularly with curved members, with variable cross sections, and/or with inelastic behaviors. Nevertheless, its theoretical equivalence to the solutions of the direct Lagrangian equations has not been examined so far. This paper presents the theoretical convergence and accuracy of the method, where an original curved element of variable cress section is considered as well as an approximate straight element of constant cross section.