Multi-objective optimal design of hybrid composite laminates for minimum cost and maximum fundamental frequency and frequency gaps

This work presents an engineering method for optimizing structures made of bars, beams, plates, or a combination of those components. Corresponding problems involve both continuous (size) and discrete (topology) variables. Using a branched multipoint approximate function, which involves such mixed variables, a series of sequential approximate problems are constructed to make the primal problem explicit. To solve the approximate problems, genetic algorithm (GA) is utilized to optimize discrete variables, and when calculating individual fitness values in GA, a second‐level approximate problem only involving retained continuous variables is built to optimize continuous variables. The solution to the second‐level approximate problem can be easily obtained with dual methods. Structural analyses are only needed before improving the branched approximate functions in the iteration cycles. The method aims at optimal design of discrete structures consisting of bars, beams, plates, or other components. Numerical examples are given to illustrate its effectiveness, including frame topology optimization, layout optimization of stiffeners modeled with beams or shells, concurrent layout optimization of beam and shell components, and an application in a microsatellite structure. Optimization results show that the number of structural analyses is dramatically decreased when compared with pure GA while even comparable to pure sizing optimization.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.5957

An engineering method for complex structural optimization involving both size and topology design variables

This paper presents a two-level approximation method for multi-objective optimization of a composite stiffened panel. The purpose is to seek the minimum structural mass and maximum fundamental frequency subject to given displacement constraints and manufacturing limitations. The design variables are the stiffener layout, and laminate stacking sequences for stiffeners and the panel skin. By introducing the concept of ground structure in both stiffener layout and laminate stacking sequence, the design problem is formulated with mixed discrete and continuous variables. Two types of discrete variables represent the existence of each stiffener and the existence of each ply in the laminate, respectively, with continuous ones for ply thicknesses. Considering the objectives are of different dimensions, a weighted min-max objective function is defined and minimized. The problem is firstly made explicit with branched multipoint approximate functions. Genetic algorithm (GA) is then adopted to optimize two types of discrete variables, determining which stiffeners/layers are deleted or retained. For fitness calculation in GA, a second-level approximation is built to optimize continuous ply thicknesses of the necessary layers that are retained. By giving different initial designs of stiffener layout and laminate stacking sequences, reasonable optimization results, which are tradeoffs between the considered two objectives, are obtained as design options. From the number of required structural analysis, it shows that the proposed method has a good efficiency in seeking rational solutions, which are tradeoffs between conflicting objectives and also feasible designs satisfying all considered constraints.

Multi-objective optimization of a composite stiffened panel for hybrid design of stiffener layout and laminate stacking sequence

Parameters in adaptive trusses considering placements of actuators, control gains as well as structure cross-sectional sizes, have been simultaneously optimized to suppress vibrations and to maintain stringent shape specifications. Since the placements of actuators are treated as (0,1) variables but the control gains and structural member sizes are continuous, the studied problem then becomes mixed (0,1)-continuous optimization, which is difficult to be tackled with conventional optimization methods since they are often encountered with local optimal solutions or numerous computational costs. A two-level multipoint approximation strategy combined with genetic algorithm, which proved to be applicable in truss topology-size optimizations involving discrete-continuous design variables, has been developed to address the current actuator placement problem. To enhance the efficiency of this method, a branched multi-point approximation function was introduced to construct the first-level approximation problem. Besides, a new fitness function as well as adaptive crossover and mutation operators were adopted to prevent the optimization process from too early converging to local optimal solutions. Numerical results were presented to illustrate the efficacy of this strategy in dealing with actuator placement problems.

Actuator placement optimization for adaptive trusses using a two-level multipoint approximation method

This paper discusses the integrated topology and sizing optimization of frame structures where beam elements are used in the structural analysis model. Based on the ground structure approach, discr...

Topology and Sizing Optimization for Frame Structures with a Two-Level Approximation Method

A two-level multipoint approximation concept is proposed. Based upon the values and the first-order derivatives of the critical constraint functions at the points obtained in the procedure of optimization, explicit functions approximating the primal constraint functions have been created. The nonlinearities of the approximate functions are controlled to be near those of the constraint functions in their expansion domains. Based on the principle above, the first-level sequence of explicitly approximate problems used to solve the primarily structural optimization problem are constructed. Each of them is approximated again by the second-level sequence of approximate problems, which are formed by using the linear Taylor series expansion and then solved efficiently with dual theory. Typical numerical examples including optimum design for trusses and frames are solved to illustrate the power of the present method. The computational results show that the method is very efficient and no intermediate/generalized design variable is required to be selected. It testifies to the adaptability and generality of the method for complex problems.

Two-level multipoint constraint approximation concept for structural optimization

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Two-level multipoint constraint approximation concept for structural optimization