A numerical method for plastic limit analysis of 3-D structures

A new displacement-based finite element is developed for thin-walled box beams. Unlike the existing elements, dealing with either static problems alone or dynamic problems only with the additional consideration of warping, the present element is useful for both static and dynamic analyses with the consideration of coupled deformation of torsion, warping and distortion. We propose to use a statically admissible in-plane displacement field for the element stiffness matrix and a kinematically compatible displacement field for the mass matrix so that the present element is useful for a wide range of beam width-to-height ratios. The axial variation of cross-sectional deformation measures is approximated by C0 continuous interpolation functions. Numerical examples are considered to confirm the validity of the present element. Copyright © 1999 John Wiley & Sons, Ltd.

Thin‐walled closed box beam element for static and dynamic analysis

Gives a bibliographical review of the finite element analyses of sandwich structures from the theoretical as well as practical points of view. Both isotropic and composite materials are considered. Topics include: material and mechanical properties of sandwich structures; vibration, dynamic response and impact problems; heat transfer and thermomechanical responses; contact problems; fracture mechanics, fatigue and damage; stability problems; special finite elements developed for the analysis of sandwich structures; analysis of sandwich beams, plates, panels and shells; specific applications in various fields of engineering; other topics. The analysis of cellular solids is also included. The bibliography at the end of this paper contains 655 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1980 and 2001.

Finite element analyses of sandwich structures: a bibliography (1980–2001)

A mixed variational principle for the limit analysis of rigid-perfectly plastic continua is discussed, in which the nonlinear yield condition and the associated flow rule appear through a suitably defined ‘penalty’ function. A mixed finite element discrete formulation is derived and a sequential unconstrained minimization technique is devised, affording a complete (static and kinematic) solution. Several results are presented in both structural and soil mechanics, compared with previously available (exact and numerical) solutions.

A mixed formulation and mixed finite elements for limit analysis

This paper deals with the one-dimensional static and dynamic analysis of thin-walled closed beams with general quadrilateral cross sections. The coupled deformations of distortion as well as torsion and warping are investigated in this work. A new approach to determine the functions describing section deformations is proposed. In particular, the present distortion function satisfies all the necessary continuity conditions unlike Vlasov's distortion function. Based on these section deformation functions, a one-dimensional theory dealing with the coupled deformations is presented. The actual numerical work is carried out using two-node C 0 finite element formulation. The present one-dimensional results for some static and free-vibration problems are compared with the existing and the plate finite element results.

Analysis of Thin-Walled Closed Beams With General Quadrilateral Cross Sections

In this study a unified approach is presented for the analysis of the shear strain effects in thin-walled beams subjected to both non-uniform bending and torsion. Middle surface shear strains are taken into account for open as well as closed cross-sections. A suitable axial displacement field is introduced by making the basic choice that the solution to the St. Venant problems is to be reproduced for v = 0 . By making use of a variational formulation, a system of differential equations is derived which rules the behaviour of a thin-walled beam with any cross-section. Hence the influence of the shear strains on the stress state as well as on the global deformation of the beam is shown through some significant examples.

Shear strain effects in flexure and torsion of thin-walled beams with open or closed cross-section

The influence of middle-surface shear strains on the dynamics of thin-walled beams is analyzed. By means of a suitable choice of the axial displacement field, shear lag effects in bending and torsion are taken into account for open and closed cross-sections. The equations of motion are obtained via Hamilton's principle. The flexural-torsional natural frequencies in the presence of warping which varies along the beam axis are compared with those given by Timoshenko-Vlasov models. The solution to the problem is pursued by means of the most natural choice, i.e. the classical trigonometric series expansion. A suitable algorithm is developed to solve the resulting eigenvalue problem which turns out to be strongly ill-conditioned.

The shear strain influence on the dynamics of thin-walled beams

As is known, when a shear core presents rows of regular openings along the height, the stiffness properties of the connecting beams can be smeared over the height by making use of concepts of statics or energy equivalence. Hence, by virtue of the constraining action of the floor slabs, the shear core can be seen as a nonhomogeneous thin‐walled beam, with open or closed (possibly multicell) cross section, constituted by an assemblage of interconnected prismatic curtains having different elastic properties. This paper presents a one‐dimensional model for the flexural‐torsional analysis of such “nonhomogeneous” thin‐walled beam with any given cross section, allowing for shear deformations due to nonuniform bending and torsion. The axial displacement field is represented by separating the cross‐sectional and axial variables, and the governing equations for the coupled flexural‐torsional behavior are given. Some examples are solved of beams with one or two planes of symmetry, showing excellent agreement with e...

Continuum model for analysis of multiply connected perforated cores

Rigid-plastic plates having a piecewise linear yield surface are studied by limit analysis. Extremum principles for the evaluation of specific dissipation power are defined by means of linear programming concepts. The law governing the plastic collapse of plates is formulated on the basis of the well-known kinematic theorem of limit analysis. A general procedure for the approximate determination of the collapse load is proposed. The paper ends with a brief numeric investigation of the uniformly loaded square plate.

Limit analysis of plates with piecewise linear yield surface

This paper discusses the dynamic loading of rigid-perfectly plastic structures by adopting a structural model discretized with constant stress finite elements. This assumption together with the hypothesis of small displacements and of a piecewise linear yield surface leads to the formulation of a problem in linear inequalities, which is, implicitly, time discretized. It is shown how the non linearity of the associated plastic flow laws leads to an equivalent extremal formulation. A numerical algorithm for solving the problem is directly derived from the mechanical statements. Numerical examples illustrate this approach. In the appendix an approximate technique is developed, which takes into account the influence of the strain-hardening and the strain rate sensitivity of material.

Ferdinando Laudiero

Papers

Shear strain effects in flexure and torsion of thin-walled beams with open or closed cross-section

The shear strain influence on the dynamics of thin-walled beams

Continuum model for analysis of multiply connected perforated cores

Limit analysis of plates with piecewise linear yield surface

On plastic dynamics of discrete structural models