Approximation-based global optimization strategy for structural synthesis
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Sepulveda, A. E.↗
Engineering topics
Schmit, L. A.
Publications and source records attributed to Schmit, L. A..
Improved approximations for control augmented structural synthesis
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Thomas, H. L.↗
An approximation based global optimization strategy for structural synthesis
A global optimization strategy for structural synthesis based on approximation concepts is presented. The methodology involves the solution of a sequence of highly accurate approximate problems using a global optimization algorithm. The global optimization algorithm implemented consists of a branch and bound strategy based on the interval evaluation of the objective function and constraint functions, combined with a local feasible directions algorithm. The approximate design optimization problems are constructed using first order approximations of selected intermediate response quantities in terms of intermediate design variables. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure setforth.
Sepulveda, A. E.↗
Synthesis of structural/control systems robust with respect to design variable tolerances
A methodology is presented for the synthesis of control augmented structures which can be modeled as an assemblage of beam, truss, and nonstructural mass elements augmented by a robust noncollocated direct output feedback control system. The control system is robust in the sense that it can tolerate manufacturing and realization errors. The robust control system is synthesized using a constraint buffering technique in conjunction with the approximation concepts approach to system synthesis. All of the design constraints on the system, including the dynamic stability, are buffered by a nonlinear quantity that is a function of acceptable tolerances on the design variables and the sensitivity of the constraints to changes in these design variables. Numerical results which illustrate the effectiveness of the method presented are given.
Thomas, H. L.↗
Control design variable linking for optimization of structural/control systems
In this study a method is presented to integrate the design space of structural/control system optimization problems in the case of state feedback control. Conventional structural sizing variables and elements of the feedback gain matrix are both treated as strictly independent design variables in the optimization by extending design variable linking concepts to the control gains. Examples which involve a variety of behavior constraints, including dynamic transient response and control force limits, are effectively solved by using the method presented.
Jin, I. M.↗
Control augmented structural synthesis with transient response constraints
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Manning, R. A.↗
Conservative buffering of approximate nonlinear constraints
In engineering design practice behavior is usually predicted based on some known nominal design. However, when the design is fabricated it will differ from the nominal design because of manufacturing tolerances. In order to generate nominal designs that will still satisfy behavior constraints in the presence of manufacturing tolerances, engineers resort to the use of safety factors, over and above those introduced to account for other uncertainties (e.g., in load conditions, material properties, analysis modeling). The accurate selection of the values of these manufacturing tolerances safety factors is dependent on the capability of the engineer to determine the sensitivity of the critical constraints to changes in the design variables. This process usually leads to overly conservative designs. The task of choosing safety factors is much more difficult in structural synthesis because: (1) it is not known which constraints will be active at the final design, (2) as the design changes during the synthesis process the sensitivities of the constraints with respect to the design variables also change, and (3) the imposition of the safety factors themselves may change the set of critical constraints. These difficulties can be overcome with the approximation concepts approach to structural synthesis by buffering the approximate constraints with quantities that are related to the design variable tolerances and the accurate sensitivities of the constraints with respect to the design variable. Designs generated by this approach tend to be feasible but not overly conservative.
Thomas, H. L.↗
Improved approximations for control augmented structural synthesis
A methodology for control-augmented structural synthesis is presented for structure-control systems which can be modeled as an assemblage of beam, truss, and nonstructural mass elements augmented by a noncollocated direct output feedback control system. Truss areas, beam cross sectional dimensions, nonstructural masses and rotary inertias, and controller position and velocity gains are treated simultaneously as design variables. The structural mass and a control-system performance index can be minimized simultaneously, with design constraints placed on static stresses and displacements, dynamic harmonic displacements and forces, structural frequencies, and closed-loop eigenvalues and damping ratios. Intermediate design-variable and response-quantity concepts are used to generate new approximations for displacements and actuator forces under harmonic dynamic loads and for system complex eigenvalues. This improves the overall efficiency of the procedure by reducing the number of complete analyses required for convergence. Numerical results which illustrate the effectiveness of the method are given.
Thomas, H. L.↗
Influence of time lag and noncolocation on integrated structural/control system designs
Recent research efforts have led to the development of simultaneous structural/control system design procedures. Absent in any of the work is the time delay present in the control system sensors and actuators and the computational time delay for synthesizing actuator commands from sensor measurements. Madden has shown that the time delay present in the control system can have profound effects on the resulting system performance and stability regardless of its source. In addition, many of the simultaneous structural/control system design procedures have used colocated sensors and actuators for implementation of the control system. In actual practice, colocation in not always possible. The issue of stability degradation when using noncolocated sensor and actuators was raised. The integrated structural/control system design procedure is extended to include the effects of time lag and noncolocation of sensors and actuators on the resulting optimum designs.
Manning, R. A.↗
An integrated approach to the synthesis of geometrically non-linear structures
An integrated approach to the minimum weight design of geometrically nonlinear three-dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The nonlinear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the constraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically nonlinear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.
Smaoui, H.↗
Control-augmented structural synthesis
A control-augmented structural synthesis methodology is presented in which the structural member sizes and active control system feedback gains are treated simultaneously as independent design variables. Multiple static and harmonic dynamic loading conditions are considered. Constraints are imposed on static displacements, natural frequencies, and the magnitudes of the steady-state dynamic displacements and actuator forces to ensure acceptable system behavior. Side constraints imposed on the design variables protect against the generation of unrealizable designs. Example problems are presented that demonstrate the method and underscore the importance of integrating the structural and active control system design process.
Lust, R. V.↗
Advances in dual algorithms and convex approximation methods
A new algorithm for solving the duals of separable convex optimization problems is presented. The algorithm is based on an active set strategy in conjunction with a variable metric method. This first order algorithm is more reliable than Newton's method used in DUAL-2 because it does not break down when the Hessian matrix becomes singular or nearly singular. A perturbation technique is introduced in order to remove the nondifferentiability of the dual function which arises when linear constraints are present in the approximate problem.
Smaoui, H.↗
Behavior sensitivities for control augmented structures
During the past few years it has been recognized that combining passive structural design methods with active control techniques offers the prospect of being able to find substantially improved designs. These developments have stimulated interest in augmenting structural synthesis by adding active control system design variables to those usually considered in structural optimization. An essential step in extending the approximation concepts approach to control augmented structural synthesis is the development of a behavior sensitivity analysis capability for determining rates of change of dynamic response quantities with respect to changes in structural and control system design variables. Behavior sensitivity information is also useful for man-machine interactive design as well as in the context of system identification studies. Behavior sensitivity formulations for both steady state and transient response are presented and the quality of the resulting derivative information is evaluated.
Manning, R. A.↗
Control augmented structural synthesis with transient response constraints
An integrated approach to the optimum design of control augmented structural systems is presented in which structural variables and control variables are changed simultaneously during the design process. Constraints are imposed on peak transient dynamic displacements and accelerations, static displacements, natural frequencies, and control system effort. Side constraints imposed on structural member sizes and control system thresholds and actuator output forces insure the generation of physically meaningful designs. Example problems are presented which bring out the benefits of simultaneous treatment of both the structural design variables and the control design variables.
Manning, R. A.↗
Alternative approximation concepts for space frame synthesis
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Lust, R. V.↗
Alternative approximation concepts for space frame synthesis
A structural synthesis methodology for the minimum mass design of 3-dimensionall frame-truss structures under multiple static loading conditions and subject to limits on displacements, rotations, stresses, local buckling, and element cross-sectional dimensions is presented. A variety of approximation concept options are employed to yield near optimum designs after no more than 10 structural analyses. Available options include: (A) formulation of the nonlinear mathematcal programming problem in either reciprocal section property (RSP) or cross-sectional dimension (CSD) space; (B) two alternative approximate problem structures in each design space; and (C) three distinct assumptions about element end-force variations. Fixed element, design element linking, and temporary constraint deletion features are also included. The solution of each approximate problem, in either its primal or dual form, is obtained using CONMIN, a feasible directions program. The frame-truss synthesis methodology is implemented in the COMPASS computer program and is used to solve a variety of problems. These problems were chosen so that, in addition to exercising the various approximation concepts options, the results could be compared with previously published work.
Lust, R. V.↗
Structural optimization with dynamic behavior constraints
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Mills-Curran, W. C.↗
Alternative approximation concepts for space frame synthesis
A method for space frame synthesis based on the application of a full gamut of approximation concepts is presented. It is found that with the thoughtful selection of design space, objective function approximation, constraint approximation and mathematical programming problem formulation options it is possible to obtain near minimum mass designs for a significant class of space frame structural systems while requiring fewer than 10 structural analyses. Example problems are presented which demonstrate the effectiveness of the method for frame structures subjected to multiple static loading conditions with limits on structural stiffness and strength.
Lust, R. V.↗