TY - JOUR

T1 - Discrete-continuous variable structural optimization of systems under stochastic loading

AU - Jensen, Hector A.

AU - Beer, Michael

N1 - Funding Information: The research reported here was supported in part by CONICYT under Grant No. 1070903 which is gratefully acknowledged by the authors. The authors are also grateful for the partial financial support by National University of Singapore through the Ministry of Education Academic Research Fund , Grant No. R264000234133 .

PY - 2010/9

Y1 - 2010/9

N2 - The paper deals with the optimization of structural systems involving discrete and continuous sizing type of design variables. In particular, the reliability-based optimization of non-linear systems subject to stochastic excitation where some or all of the design variables are discrete is considered. The reliability-based optimization problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The probability that design conditions are satisfied within a given time interval is used as measure of system reliability. The basic mathematical programming statement of the structural optimization problem is converted into a sequence of explicit approximate primal problems of separable form. The explicit approximate primal problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple non-negativity constraints on the dual variables. A gradient projection type of algorithm is used to find the solution of each dual problem. The effectiveness of the method is demonstrated by presenting a numerical example of a non-linear system subject to stochastic ground acceleration.

AB - The paper deals with the optimization of structural systems involving discrete and continuous sizing type of design variables. In particular, the reliability-based optimization of non-linear systems subject to stochastic excitation where some or all of the design variables are discrete is considered. The reliability-based optimization problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The probability that design conditions are satisfied within a given time interval is used as measure of system reliability. The basic mathematical programming statement of the structural optimization problem is converted into a sequence of explicit approximate primal problems of separable form. The explicit approximate primal problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple non-negativity constraints on the dual variables. A gradient projection type of algorithm is used to find the solution of each dual problem. The effectiveness of the method is demonstrated by presenting a numerical example of a non-linear system subject to stochastic ground acceleration.

KW - Approximation concepts

KW - Dual formulation

KW - Non-linear systems

KW - Reliability-based optimization

KW - Sensitivity analysis

UR - http://www.scopus.com/inward/record.url?scp=77953543500&partnerID=8YFLogxK

U2 - 10.1016/j.strusafe.2010.03.007

DO - 10.1016/j.strusafe.2010.03.007

M3 - Article

AN - SCOPUS:77953543500

VL - 32

SP - 293

EP - 304

JO - Structural safety

JF - Structural safety

SN - 0167-4730

IS - 5

ER -