An optimal design of FE structures with limited ductility

The minimum volume design of elastic perfectly plastic FE structures subjected to quasi-static fixed and cyclic loads is searched in such a way that the structure remains into the elastic field in serviceability conditions, while it is subjected to alternating plasticity under very strong cyclic actions, incremental and instantaneous collapse being prevented. In order to take into account the limited ductility of the material, suitable chosen limits on the plastic deformations related to the initial transient phase and/or to the subsequent steady-state phase are considered for the structure subjected to very strong cyclic actions. A numerical application confirm the theoretical expectations…

A plastic shakedown design of FE structures with constraints on deformations

Bounds on transient phase plastic deformations in optimal design of steel frames subjected to cyclic loads

A minimum volume multicriterion design of elastic perfectly plastic steel frames subjected to a combination of quasi-static fixed and cyclic loads, bounding the transient phase plastic deformations, is proposed. The problem is formulated according to a plastic shakedown criterion, so that incremental and instantaneous collapse are certainly prevented when the frame is subjected to very strongly amplified cyclic loads. The further condition that the structure must also behave elastically in serviceability conditions is imposed. Since the steady-state loading history is known it is possible to directly bound the steady-state plastic deformations. By applying a suitable own bounding theorem, i…

Discrete Structure Shakedown Design Ices ’95, Hawai, July 30 – August 3, 1995

The minimum volume shakedown design problem was already approached by several authors with studies devoted to discrete structures (see e.g. [1]–[5]) and to continuous structures (see e.g. [6]). Except some very simple structural typologies, also the optimal shakedown design problem formulations for continuous structures need to be discretized in the application stage. In any case, the relevant optimal shakedown design problem for discrete (or discretized) structures is formulated in terms of design variables as well as behavioural variables, and consists in the search for the/a minimum volume design among all feasible designs (i.e. able to shakedown). Due to its strong non-linearity, the la…

A multicriterion design of steel frames with shakedown constraints

The minimum volume design of elastic perfectly plastic steel frames subjected to fixed and cyclic loads is searched in such a way that the structure remains in elastic field in serviceability conditions, while it is subjected to alternating plasticity under very strong cyclic actions, incremental and instantaneous collapse being prevented. The problem is faced on the grounds of a statical and a kinematical approach. The Kuhn-Tucker conditions of the two problems prove that they are each one the dual of the other and provide useful pieces of information about the structural behaviour. Numerical applications confirm the theoretical expectations: optimal designs turn out to be quite light, wit…

Progetto ad adattamento plastico di strutture ad elementi finiti

An Iterative Approach to Dynamic Elastic-Plastic Analysis

The step-by-step analysis of structures constituted by elastic-plastic finite elements, subjected to an assigned loading history, is here considered. The structure may possess dynamic and/or not dynamic degrees-of-freedom. As it is well-known, at each step of analysis the solution of a linear complementarity problem is required. An iterative method devoted to solving the relevant linear complementarity problem is presented. It is based on the recursive solution of a linear complementarity, problem in which the constraint matrix is block-diagonal and deduced from the matrix of the original linear complementarity problem. The convergence of the procedure is also proved. Some particular cases …

An optimal design of elastic plastic structures with bounds on transient and steady-state plastic deformations

Elastic plastic analysis iterative solution

The step-by-step analysis of finite element elastic plastic structures subjected to an assigned (quasi-static) loading history, is considered; it identifies with the well-known sequence of linear complementarity problems. An iterative technique devoted to solve the relevant linear complementarity problem is presented. It is based on the recursive solution of a suitable linear complementarity problem, deduced from the relevant one and easier than it. The procedure convergency is proved. Some noticing particular cases are examined. The physical meaning of the procedure is shown to be a plastic relaxation. The suitable numerical ranges for some check parameter values, to be utilized in the app…