Topology optimization for the seismic design of truss-like structures (original) (raw)
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Optimum design of nonlinear space trusses
Computers & Structures, 1988
Abstrnct-The structural optimization algorithms developed in recent years mainly consider the elastic behaviour of structures. The reserve of resisting loads in nonlinear regions is totally ignored. The optimum design algorithm presented in this study takes into account the response of the structure beyond the elastic limit. This is achieved by coupling a nonlinear analysis technique with an optimality criteria approach. The first is used to provide the nonlinear behaviour of the structure as the design variables are changed. The latter is employed to obtain a recursive relationship to be utilized to update these design variables. The design algorithm iricludes the displacement limitations. Consideration of the post buckling and post yielding behaviour of the truss members makes the necessity of stress and buckling constraints irrelevant. Minimum size constraints are imposed on the design variables. A number of design examples are presented to demonstrate the application of the method.
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 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.
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
Optimization of geometrically nonlinear truss structures under dynamic loading
REM - International Engineering Journal, 2020
The goal of this article is to present the formulation of the optimization problem of truss structures with geometric nonlinearity under dynamic loads and provide examples of this problem. The formulated optimization problem aims to determine the cross-sectional area of the bars that minimizes the weight of the structure, imposing constraints on nodal displacements and axial stresses. To solve this problem, computational routines were developed in MATLAB ® using Sequential Quadratic Programming (SQP), the algorithm of which is available on MATLAB's Optimization Toolbox™. The nonlinear finite space truss element is described by an updated Lagrangian formulation. The geometric nonlinear dynamic analysis performed combines the Newmark method with Newton-Raphson iterations. It was validated by a comparison with solutions available in literature and with solutions generated by the ANSYS ® software. Optimization examples of trusses under different dynamic loading were studied considering their geometric nonlinearity. The results indicate a significant reduction in structure weight for both undamped and damped cases.
New displacement-based methods for optimal truss topology design
32nd Structures, Structural Dynamics, and Materials Conference, 1991
In this paper we present two alternate methods for maximum stiffness truss topology design. The ground structure approach is used, and the problem is formulated in. terms of displacements and bar areas. This large, non-convex optimization problem can be solved by a simultaneous analysis and design approach. Alternatively, an equivalent, unconstrained and convex problem in the displacements only can be formulated, and this problem can be solved by a non-smooth, steepest descent algorithm. In both methods we circumvent the explicit solving of the equilibrium equations and the assembly of the global stiffness matrix. A large number of examples have been studied, showing the attractive features of topology design as well as exposing interesting features of optimal topologies.
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.
Structural Topology Optimization with Stress Constraint Considering Loading Uncertainties
Periodica Polytechnica Civil Engineering, 2015
This paper deals with the consideration of loading uncertainties in topology optimization via a fundamental optimization problem setting. Variability of loading in engineering design is realized e.g. in the action of various load combinations. In this study this phenomenon is modelled by the application of two mutually excluding (i.e. alternating) forces such that the magnitudes and directions are varied parametrically in a range. The optimization problem is stated as to find the minimum volume (i.e. the minimum weight) load-bearing elastic truss structure that transfers such loads acting at a fix point of application to a given line of support provided that stress limits are set. The aim of this paper is to numerically determine the layout, size, and volume of the optimal truss and to support the numerical results by appropriate analytical derivations. We also show that the optimum solution is non-unique, which affects the static determinacy of the structure as well. In this paper we also create a truss-like structure with rigid connections based on the results of the truss optimization and analyse it both as a bar structure (frame model) and a planar continuum (disk) structure to compare with the truss model. The comparative investigation assesses the validity of computational models and proves that the choice affects design negatively since rigidity of connections resulted by usual construction technologies involve extra stresses leading to significant undersizing.
Revista de la construcción, 2020
The objective of this paper is to present the formulation for optimizing truss structures with geometric nonlinearity under dynamic loads, provide pertinent case studies and investigate the influence of damping on the final result. The type of optimization studied herein aims to determine the cross-sectional areas that will minimize the weight of a given structural system, by imposing constraints on nodal displacements and axial stresses. The analyses are carried out using Sequential Quadratic Programming (SQP), available in MATLAB’s Optimization Toolbox™. The nonlinear finite space truss element is defined with an updated Lagrangian formulation, and the geometrically nonlinear dynamic analysis performed herein combines the Newmark method with Newton-Raphson iterations. The dynamic analysis approach was validated by comparing the results obtained with solutions available in the literature as well as with numerical models developed with ANSYS® 18.2. A number of optimization examples ...
Shape optimization of structures under earthquake loadings
Structural and Multidisciplinary Optimization, 2013
The optimum design of structures under static loads is well-known in the design world; however, structural optimization under dynamic loading faces many challenges in real applications. Issues such as the time-dependent behavior of constraints, changing the design space in the time domain, and the cost of sensitivities could be mentioned. Therefore, optimum design under dynamic loadings is a challenging task. In order to perform efficient structural shape optimization under earthquake loadings, the finite element-based approximation method for the transformation of earthquake loading into the equivalent static loads (ESLs) is proposed. The loads calculated using this method are more accurate and reliable than those obtained using the building regulations. The shape optimization of the structures is then carried out using the obtained ESLs. The proposed methodologies are transformed into user-friendly computer code, and their capabilities are demonstrated using numerical examples.