New displacement-based methods for optimal truss topology design (original) (raw)

Optimization methods for truss geometry and topology design

Structural Optimization, 1994

Truss topology design for minimum external work (compliance) can be expressed in a number of equivalent potential or complementary energy problem formulations in terms of member forces, displacements and bar areas. Using duality principles and non-smooth analysis we show how displacements only as well as stresses only formulations can be obtained and discuss the implications these formulations have for the construction and implementation of efficient algorithms for large-scale truss topology design. The analysis covers min-max and weighted average multiple load designs with external as well as self-weight loads and extends to the topology design of reinforcement and the topology design of variable thickness sheets and sandwich plates. On the basis of topology design as an inner problem in a hierarchical procedure, the combined geometry and topology design of truss structures is also considered. Numerical results and illustrative examples are presented.

Using optimization to solve truss topology design problems

Inv. Op, 2005

The design of truss structures is an important engineering activity which has traditionally been done without optimization support. Nowadays we witness an increasing concern for efficiency and therefore engineers seek aid on Mathematical Programming to optimize a design. In this article, we consider a mathematical model where we maximize the stiffness with a volume constraint and bounds in the cross sectional area of the bars, [2]. The basic model is a large-scale non-convex constrained optimization problem but two equivalent problems are considered. One of them is a minimization of a convex non-smooth function in several variables (much less than in the basic model), being only one non-negative. The other is a semidefinite programming problem. We solve some instances using both alternatives and we present and compare the results.

Optimal Design of Trusses with Account for Topology Variation∗

Mechanics of Structures and Machines, 1998

In this paper, a heuristic algorithm is presented for optimal design of trusses with varying cross-sectional parameters, configuration of nodes, and number of nodes and bars. The algorithm provides new nodes and bars at some states and for the optimal truss configuration. It is assumed that the structure evolves with the overall size parameter and a "bifurcation" of topology occurs with the generation of new nodes, in order to minimize the cost function. Both displacement and stress constraints can be introduced in the optimization procedure. 'Communicated by E.1. Haug

Topology Optimization of Truss

The optimal design of skeletal structure becomes imperative both from engineering and cost considerations in recent year. Total cost of the structure mainly depends on weight of the structure and weight of the structure is proportional to material distribution within the structure.

Convex topology optimization for hyperelastic trusses based on the ground-structure approach

Structural and Multidisciplinary Optimization, 2014

Most papers in the literature, which deal with topology optimization of trusses using the ground structure approach, are constrained to linear behavior. Here we address the problem considering material nonlinear behavior. More specifically, we concentrate on hyperelastic models, such as the ones by Hencky, Saint-Venant, Neo-Hookean and Ogden. A unified approach is adopted using the total potential energy concept, i.e., the total potential is used both in the objective function of the optimization problem and also to obtain the equilibrium solution. We proof that the optimization formulation is convex provided that the specific strain energy is strictly convex. Some representative examples are given to demonstrate the features of each model. We conclude by exploring the role of nonlinearities in the overall topology design problem.

Optimal topology and configuration design of trusses with stress and buckling constraints

Structural Optimization, 1999

A heuristic algorithm for optimal design of trusses is presented with account for stress and buckling constraints. The design variables are constituted by cross-sectional areas, configuration of nodes and the number of nodes and bars. Similarly to biological growth models, it is postulated that the structure evolves with the characteristic size parameter and the "bifurcation" of topology occurs with the generation of new nodes and bars in order to minimize the cost function. The first-order sensitivity derivatives provide the necessary information on topology variation and the optimality conditions for configuration and cross-sectional parameters.

Topology optimization for the seismic design of truss-like structures

Computers & Structures, 2011

A practical optimization method is applied to design nonlinear truss-like structures subjected to seismic excitation. To achieve minimum weight design, inefficient material is gradually shifted from strong parts to weak parts of a structure until a state of uniform deformation prevails. By considering different truss structures, effects of seismic excitation, target ductility and buckling of the compression members on optimum topology are investigated. It is shown that the proposed method could lead to 60% less structural weight compared to optimization methods based on elastic behaviour and equivalent static loads, and is efficient at controlling performance parameters under a design earthquake.

Truss geometry and topology optimization with global stability constraints

Structural and Multidisciplinary Optimization

In this paper, we introduce geometry optimization into an existing topology optimization workflow for truss structures with global stability constraints, assuming a linear buckling analysis. The design variables are the cross-sectional areas of the bars and the coordinates of the joints. This makes the optimization problem formulations highly nonlinear and yields nonconvex semidefinite programming problems, for which there are limited available numerical solvers compared with other classes of optimization problems. We present problem instances of truss geometry and topology optimization with global stability constraints solved using a standard primal-dual interior point implementation. During the solution process, both the cross-sectional areas of the bars and the coordinates of the joints are concurrently optimized. Additionally, we apply adaptive optimization techniques to allow the joints to navigate larger move limits and to improve the quality of the optimal designs.

Optimization of Truss Structures Under Arbitrary Constraints

This paper discusses a new structural optimization method and its application to the weight minimization of truss structures under arbitrary constraints. The method reflects the idea of a synergy between Lagrange/optimality criteria applied for a single constraint and mathematical optimization methods in the following way: The single-constraint solutions are utilized to obtain a "good" ("in the convex neighborhood of the global optimum) estimate of the global solution, which can -then-be used as initial or starting point for the application of a mathematical optimization procedure. The above target is achieved applying a "max-k!' method, which is explained in the paper. Test cases illustrate the performance of the proposed methodology. The results are very satisfactory, opening the way for a further application of the method to other structural optimization problems.