A stress-based approach to the optimal design of structures with unilateral behavior of material or supports

in Structural and Multidisciplinary Optimization (2012), 46(3), 369-384

The paper deals with a formulation for the topology optimization of elastic structures that aims at minimizing the structural weight subject to compliance and local stress constraints. The global ... [more ▼]

The paper deals with a formulation for the topology optimization of elastic structures that aims at minimizing the structural weight subject to compliance and local stress constraints. The global constraint provides the expected stiffness to the optimal design while a selected set of local enforcements require feasibility with respect to the assigned strength of material. The Drucker–Prager failure criterion is implemented to handle materials with either equal or unequal behavior in tension and compression. A suitable relaxation of the equivalent stress measure is implemented to overcome the difficulties related to the singularity problem. Numerical examples are presented to discuss the features of the achieved optimal designs along with performances of the adopted procedure. Comparisons with pure compliance–based or pure stress–based strategies are also provided to point out differences arising in the optimal design with respect to conventional approaches, depending on the assumed material behavior. [less ▲]

An augmented Lagrangian optimization method for inflatable structures analysis problems

in Structural and Multidisciplinary Optimization (2006), 32(5), 383-395

This paper describes the development of an augmented Lagrangian optimization method for the numerical simulation of the inflation process in the design of inflatable space structures. Although the Newton ... [more ▼]

This paper describes the development of an augmented Lagrangian optimization method for the numerical simulation of the inflation process in the design of inflatable space structures. Although the Newton-Raphson scheme was proven to be efficient for solving many nonlinear problems, it can lead to lack of convergence when it is applied to the simulation of the inflation process. As a result, it is recommended to use an optimization algorithm to find the minimum energy configuration that satisfies the equilibrium equations characterizing the final shape of the inflated structure subject to an internal pressure. On top of that, given that some degrees of freedom may be linked, the optimum may be constrained, and specific optimization methods for constrained problems must be considered. The paper presents the formulation and the augmented Lagrangian method (ALM) developed in SAMCEF Mecano for inflatable structures analysis problems. The related quasi-unconstrained optimization problem is solved with a nonlinear conjugate gradient method. The Wolfe conditions are used in conjunction with a cubic interpolation for the line search. Equality constraints are considered and can be easily treated by the ALM formulation. Numerical applications present simulations of unconstrained and constrained inflation processes (i.e., where the motion of some nodes is ruled by a rigid body element restriction and/or problems including contact conditions). [less ▲]

Note on topology optimization of continuum structures including self-weight

in Structural and Multidisciplinary Optimization (2005), 29(4), 245-256

This paper proposes to investigate topology optimization with density-dependent body forces and especially self-weight loading. Surprisingly the solution of such problems cannot be based on a direct ... [more ▼]

This paper proposes to investigate topology optimization with density-dependent body forces and especially self-weight loading. Surprisingly the solution of such problems cannot be based on a direct extension of the solution procedure used for minimum-compliance topology optimization with fixed external loads. At first the particular difficulties arising in the considered topology problems are pointed out: non-monotonous behaviour of the compliance, possible unconstrained character of the optimum and the parasitic effect for low densities when using the power model (SIMP). To get rid of the last problem requires the modification of the power law model for low densities. The other problems require that the solution procedure and the selection of appropriate structural approximations be revisited. Numerical applications compare the efficiency of different approximation schemes of the MMA family. It is shown that important improvements are achieved when the solution is carried out using the gradient-based method of moving asymptotes (GBMMA) approximations. Criteria for selecting the approximations are suggested. In addition, the applications also provide the opportunity to illustrate the strong influence of the ratio between the applied loads and the structural weight on the optimal structural topology. [less ▲]

First and second order convex approximation strategies in structural optimization

in Structural and Multidisciplinary Optimization (1989), 1(1), 3-10

In this paper, various methods based on convex approximation schemes are discussed, that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex ... [more ▼]

In this paper, various methods based on convex approximation schemes are discussed, that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex linearization method (CONLIN) is briefly described, as well as one of its recent generalizations, the method of moving asymptotes (MMA). Both CONLIN and MMA can be interpreted as first order convex approximation methods, that attempt to estimate the curvature of the problem functions on the basis of semi-empirical rules. Attention is next directed toward methods that use diagonal second derivatives in order to provide a sound basis for building up high quality explicit approximations of the behaviour constraints. In particular, it is shown how second order information can be effectively used without demanding a prohibitive computational cost. Various first and second order approaches are compared by applying them to simple problems that have a closed form solution. [less ▲]