D. Lamblin

Variational formulation of the optimal plastic design of circular plates

Abstract The problem of minimum-cost design of rigid-plastic circular plates under axysymmetric loading is studied by the variational approach. The optimality condition is discussed for “absolute” minimum-cost design as well as for design with technological constraints. A unified and fairly comprehensive treatment of these problems is presented.

Finite element iterative method for optimal elastic design of circular plates

Abstract An iterative procedure is presented for the optimal elastic design of circular or annular plates under axisymmetric loads. The deflection or slope at a given radius is prescribed, and technological constraints are taken into account. Some examples are discussed.

Baseplate column connection under bending: Experimental and numerical study

Abstract In the past baseplate column connections have not received much attention from scientists. Only very simple elastic or plastic models are in common use for moment resisting bases. The aim of this paper is to present some experimental and numerical study for such a connection. Unstiffened rectangular baseplates with constant shape have been welded to different types of columns with square, rectangular, circular, channel and I cross-section. The assembly was then connected to a concrete foundation with four anchorage bolts and submitted to pure bending till the baseplate failed. Experimental applied bending moment curves versus deflections were recorded and the plastic behaviour of the baseplate was identified. The failure mechanism was approximated by yield-line analysis and the plastic moment was obtained. The kinamatic study was completed by a static study with a non-linear finite element program taking account: • - material and geometrical non-linear behaviour of the baseplate; • - non-linear contact with concrete foundation. • Comparison between theory and experiment is made and practical conclusions are obtained.

Minimum-Weight Plastic Design of Continuous Beams Subjected to One Single Moveable Load

Abstract The purpose of this paper is to obtain analytically minimum-weight plastic designs of simply supported continuous beams subjected to one single moveable load. The designs are established for ideal sandwich beams made of a rigid perfectly plastic material, on the basis of the sufficient condition for minimum-weight given by Save and Prager (6). The obtained minimum-weight designs are compared with plastic designs of beams with constant cross section.

On the safety of optimized structures

Confidence of designers in the theory of structural optimization is of fundamental importance for practical applications. The so-called “erosion of optimal designs” is discussed from this point of view, in the context of ring and plate examples for which the limit and post-limit behaviors are obtained either experimentally or by numerical simulations of experiments. Tentative conclusions are suggested.

Limit Analysis of Circular Cylindrical Shells under Hydrostatic Pressure

ABSTRACT The problem of limit analysis of circular cylindrical shells under hydrostatic pressure is dealt with. On the basis of Hodge plastic yield condition, solutions are achieved by solving systems of simultaneous algebraic nonlinear equations. Several cases of different boundary conditions are considered.

Application of linear programming to the optimal plastic design of circular plates subject to technological constraints

Abstract This paper is concerned with plastic minimum-volume design of circular or annular plates under axially symmetric loading. Accordingly, all characteristics of the plate depend only on the radial coordinate r . The plate is divided into rings of constant yield moment. Other technological constraints may be added, for instance bounds on the yield moments of the rings. Linear programming is used to obtain an approximate solution of the problem, and the optimality criteria are derived from the duality relations. The method is illustrated by examples which show that it is quite accurate.

Geometrical interpretation for error estimation in finite element analysis

Abstract Geometrical interpretation for the error estimation procedure in finite element analysis is discussed. The proposed description is based on the superconvergent properties of certain points in the finite element model and discrete geometrical objects which are characteristic for a discrete representation. The new local error estimator is valid for triangular and quadrilateral elements, and is strictly bounded in both nonsingular and singular cases. Preliminary calculations indicate that the new error estimator can be applied for adaptive refinement analysis especially in geometrically nonlinear shell problems where the control of both physical and geometrical fields in adaptive calculations is very important.

Interaction Curves for Bending and Axial Forces of Perfectly Plastic Curved I-Beams

ABSTRACT This paper is concerned with the ultimate strength of curved beams with an I-shaped cross section subjected to combined bending moment and axial forces. The considered cross section is assumed to be fully plastic. The corresponding statically admissible distributions of stresses result in an axial force and bending moment which generate the interaction curve. This curve may be very different from the interaction curve of a straight beam with the same cross section.

Limit analysis of cylindrical shell with reinforcing rings

Abstract This paper considers a long, perfectly plastic, cylindrical shell subjected to uniform internal pressure in the absence of longitudinal load. It is reinforced by rings with rectangular or T-cross-sections. Its limit pressure is obtained on the basis of a discrete representation of the reinforcing rings, taking into account their strong curvature. It is shown that simple parameters suffice to describe the results obtained, and are presented in graph form, together with a numerical example.