Integrated optimal structural and vibration control design

An integrated design procedure which is composed of structural design, control design, and actuator locations design is proposed in this paper. First, a composite objective function, formed by a structural and a control objective, is optimized in steady state through the homogenization design method. Then an independent modal space control algorithm (IMSC) is performed on this optimal structure to reduce the dynamic response. Finally, to minimize the control force while still obtaining the same modal response for the controlled modes, the optimal choice for actuator locations is discussed.Part of this paper was presented in the First World Congress of Structural and Multidisciplinary Optimization (held in Goslar, Germany, May 28–June 2, 1995).     

Optimization of nonhomogeneous facesheets in composite sandwich plates

The optimal design of composite sandwich plates in which the facesheets are composed of a carbon fiber/epoxy net is considered. The objective of the work is to obtain minimum mass designs while maintaining constraints on the first natural frequency and selected facesheet stress components. The facesheets are assumed to be composed of an orthotropic net of unidirectional composite fiber strips and the optimal design (the least mass design) is achieved by changing the strip widths and the spacings between them. It is demonstrated that varying the spatial fiber strip distribution can lead to significant structural advantages; in the example presented, a 32% facesheet mass reduction is achieved.     

Optimal design of laminated composite beam structures

This work deals with design sensitivity analysis and optimal design of composite structures modelled as thin-walled beams. The structures are treated as a torsion-bending resistant beams. The analysis problem is discretized by a finite element technique. A two-node Hermitean beam element is used. The beam sections are made from an assembly of elements that correspond to flat layered laminated composite panels. Optimal design is performed with respect to the lamina orientations and thickness of the laminates. The structural weight is considered as the objective function. Constraints are imposed on stresses, displacements, critical load and natural frequencies. Two failure criteria are used to limit the structural strength: Tsai-Hill and maximum stress. The Tsai-Hill criterion is also adopted to predict the first-ply-failure loads. The design sensitivity analysis is analytically formulated and implemented. An adjoint variable method is used to derive the response sensitivities with respect to the design. A mathematical programming approach is used for the optimization process. Numerical examples are performed on three-dimensional structures.     

Integrated design of an adaptive neurocontroller for a 2-D aeroelastic system

The design of control configured structures has been considered in a number of recent studies. Both active and passive measures for structural vibration control have been examined in this context. The present paper addresses issues related to the use of neural network based control systems in such applications. A simplified 2-D representation of an aeroelastic system, consisting of an airfoil with a trailing-edge flap, comprises the test bed for the present study. With a proper selection of structural spring characteristics, and choice of unsteady aerodynamic forces and moments, the system provides a rudimentary 2-D model of a helicopter rotor blade that includes both structural and aerodynamic nonlinearities. The integrated optimal desisgn of the plant and its control system for optimized response under disturbance loading is the principle objective of the design exercise. The focus of the paper is three-fold — it establishes the justifiction for replacing traditional control systems with neurocontrollers in such problems, examines issues related to an integrated structural-control design strategy, and discusses a detailed implementation of the approach in a linearized 2-D aeroelastic system. The design problem contains multiple relative optima, and the use of a genetic algorithm (GA) based optimization procedure is shown to be an effective tool to locate the optimal design. Results from numerical experiments are presented in support of the proposed design approach.     

Optimization of passive vibration isolators mechanical characteristics

The contribution of optimization has been essential to the more recent developments in design of new mechanical structures and materials. The objective of this work is to apply the models of material and structural optimization to the design of passive vibration isolators. A computational tool to identify the optimal viscoelastic characteristics of a nonlinear one-dimensional isolator was developed. The cost functional involves the minimization of a weighted average of the maximum transient and steady state response amplitudes for a set of predefined dynamic loads. The optimal isolator behaviour is obtained by a simulated annealing method. The solutions obtained are analyzed and discussed concerning their dependence on the applied forces and objective function selection. The results obtained can facilitate the design of elastomeric materials with improved behaviour in terms of dynamic stiffness for passive vibration control.     

An optimal control approach to the design of vibrating elastic-viscoelastic sandwich beams

This work features the application of an optimal control algorithm to a new class of continuous one-dimensional structural design problems. A sandwich beam of rectangular cross-section is considered. It has a variable-thickness core and two equal variable-thickness cover layers and is subjected to harmonic forced vibrations. The objective is to distribute both the core and layer mass so as to minimize a measure of dynamic compliance for forced steady-state vibration and fixed material volumes. Either or both materials may be viscoelastic. Any constitutive relation may be used provided it is linear and time-invariant.The design problem is formulated as an optimal control problem. The resulting problem contains ten state variables, two control functions, four control parameters, and six terminal state constraints. Simple transformations are used to treat the minimum-gage constraints. A conjugate gradient/gradient projection optimal control algorithm is then used to obtain numerical solutions. Several optimal beam designs are presented and compared for a variety of problem parameter values.     

Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model

Based on discrete material optimization and topology optimization technologies, this paper discusses the problem of integrated optimization design of the material and structure of fiber-reinforced composites by considering the characteristics of the discrete variable of fiber ply angle because of the manufacture requirements. An optimization model based on the minimum structural compliance with a specified composite volume constraint is established. The ply angle and the distribution of the composite material are introduced as independent variables in two geometric scales (material and structural scales). The void material is added into the optional discrete material set to realize the topology change of the structure. This paper proposes an improved HPDMO (Heaviside Penalization of Discrete Material Optimization) model to obtain a better convergent result, and an explicit sensitivity analysis is performed. The effects of the HPDMO model on the convergence rate of the optimization results, the objective function value and the iteration history are studied and compared with those from the classical Discrete Material Optimization model and the Continuous Discrete Material Optimization model in this paper. Numerical examples in this paper show that the HPDMO model can effectively achieve the integrated optimization of the fiber ply angle and its distribution in the structural domain, and can also considerably improve the convergence rate of the optimal results compared with other DMO models. This model will help to reduce the manufacture cost of the optimal design.     

Optimal design of sandwich and laminated composite plates based on the planning of experiments

Optimal design problems of sandwich plates with soft core and laminated composite face layers, and multilayered composite plates are investigated. The optimal design problems are solved by using the method of the planning of experiments. The optimization procedure is divided into the following stages: choice of control parameters and establishment of the domain of search, elaboration of plans of experiment for the chosen number of reference points, execution of the experiment, determination of simple mathematical models from the experimental data, design of the structure on the basis of the mathematical models discovered, and finally verification experiments at the point of the optimal solution. Vibration and damping analysis is performed by using a sandwich plate finite elements based on a broken line model. Damping properties of the core and face layers of the plate are taken into account in the optimal design. Modal loss factors are computed using the method of complex eigenvalues or the energy method. Frequencies and modal loss factors of the plate are constraints in the optimal design problem. There are also constraints on geometrical parameters and the bending stiffness of the plate. The mass of the plate is the objective function. Design parameters are the thickness of the plate layers. In the points of experiments computer simulation using FEM is carried out. Using this information, simple mathematical models for frequencies and modal loss factors for the plate are determined. These simple mathematical functions are used as constraints in the nonlinear programming problem, which is solved by random search and the penalty function method. Numerical examples of the optimal design of clamped sandwich and simply supported laminated composite plates are presented. A significant improvement of damping properties of a sandwich plate is observed in comparison with a simple plate of equal natural frequencies.     

Multilevel optimal design of composite structures including materials with negative Poisson's ratio

Multilevel iterative optimal design procedures, horrowed from the theory of structural optimization by means of homogenization, are used in this paper for the optimal material design of composite material structures. The method is quite general and includes materials with appropriate microstructure, which may lead eventually to phenomenological, overall negative Poisson's ratios. The benefits of optimal structural design gained by this approach, together with the first attempts to explain the taskoriented microstructure of natural structures, are investigated by means of numerical examples, and simulation of, among others, human bones.     

Robust design optimization of structures through consideration of variation

Optimal structural design is considered under the presence of variation in loading, geometry and material properties. A Monte Carlo simulation is embedded in a genetic optimization algorithm to produce an output distribution for the objective function and constraint functions at each design evaluation. A hybrid genetic/non-linear-programming algorithm is used with a multi-objective formulation to locate a design that is optimal under the primary design criteria, but is simultaneously insensitive to variation. Cross-sectional, geometric and topological design changes are considered. Specific examples presented include a truss structure and an automotive inner body panel. The goal is to produce optimal designs that map better to the designer's intent.     

Cost optimization of hybrid composite flywheel rotors for energy storage

A novel approach to composite flywheel rotor design is proposed. Flywheel development has been dominated by mobile applications where minimizing mass is critical. This technology is also attractive for various industrial applications. For these stationary applications, the design is considerably cost-driven. Hence, the energy-per-cost ratio was used as the objective function. Based on an analytical approach for calculating stresses in multi-rim hybrid composite rotors, the nonlinear optimization problem was solved using a multi-strategy optimization scheme that combines an evolutionary algorithm with a nonlinear interior-point method. The problem was solved for a sample rotor with varying cost ratio of the rim materials. Instead of an optimal solution per cost ratio, only four optimal designs were obtained with a sharp transition between designs at specific cost ratios. This sharp transition is explained by the intricate interplay that exists between the objective function and the nonlinear constraints imposed by the applied failure criteria.     

Optimum design of a first story damping system

The optimum design of a first story damping system of multistory shear type structures is considered. Analytical expressions, for the case of stationary white noise ground accelerations, are derived for maximum displacements of each floor. Based on these, suitable objective functions are defined. Parametric study for the determination of the effect of structural damping and structure's flexibility on the control quantities is performed and the optimal design of several structures is carried out.     

Reliability-based multiobjective optimization for automotive crashworthiness and occupant safety

This paper presents a methodology for reliability-based multiobjective optimization of large-scale engineering systems. This methodology is applied to the vehicle crashworthiness design optimization for side impact, considering both structural crashworthiness and occupant safety, with structural weight and front door velocity under side impact as objectives. Uncertainty quantification is performed using two first order reliability method-based techniques: approximate moment approach and reliability index approach. Genetic algorithm-based multiobjective optimization software GDOT, developed in-house, is used to come up with an optimal pareto front in all cases. The technique employed in this study treats multiple objective functions separately without combining them in any form. It shows that the vehicle weight can be reduced significantly from the baseline design and at the same time reduce the door velocity. The obtained pareto front brings out useful inferences about optimal design regions. A decision-making criterion is subsequently invoked to select the “best” subset of solutions from the obtained nondominated pareto optimal solutions. The reliability, thus computed, is also checked with Monte Carlo simulations. The optimal solution indicated by knee point on the optimal pareto front is verified with LS-DYNA simulation results.     

On the design optimization of built-up stiffened steel beams with buckling and frequency constraints

The literature on the structural design optimization of steel-plate girders indicates a need for more refined research studies to obtain optimal designs by formulating and solving the design problem that combines structural sizing and shape parameters in one unified, constrained problem. For this purpose, the structural optimization design problem of stiffened steel-plate girders is formulated with specified loading conditions and constraints on strength and serviceability considerations including limits on fundamental frequency and buckling modes. The finite-element method-based model is used to define the objective function and the structural/geometric response functions, while the geometric domain elements are used to systematically perturb the structural shape during the search for an optimal shape of the structure. The mathematical statement of the gradient-based-design problem is solved for an optimal structural size and shape with buckling and frequency constraints in addition to the traditional strength constraints. The numerical results obtained are compared with results obtained from a less formal ad hoc design procedure, and some conclusions are drawn to emphasize the design benefits obtained from solving the design problem for optimal structural size and shape.     

Robust optimal parametric LQ control with a guaranteed cost bound and applications

For an optimal parametric linear quadratic (LQ) control problem, a design objective is to determine a controller of constrained structure such that the closed-loop system is asymptotically stable and an associated performance measure is optimized. In the presence of system uncertainty, the system via a parametric LQ design is further required to be robust in terms of maintaining the closed-loop stability with a guaranteed cost bound. This problem is referred to as ‘robust optimal parametric LQ control with a guaranteed cost bound’ and is addressed in this work. A new design method is proposed to find an optimal controller for simultaneously guaranteeing robust stability and performance over a specified range of parameter variations. The results presented generalize some previous work in this area. A versatile numerical algorithm is also given for computing the robust optimal gains. The usefulness of the design method is demonstrated by numerical examples and a design of the robust control of a VTOL helicopter.     

Performance assessment of advanced supervisory-regulatory control systems with subspace LQG benchmark

In this paper, a subspace method for LQG design and performance assessment is proposed for control systems in which supervisory and regulatory controllers are employed in a cascade structure. Usually, this is the case when an advanced controller is used in a supervisory control layer on the top of the regulatory control system, resulting in a cascade control structure. The objective of this study is to provide the optimal LQG control design in the cascade control structure and also to propose a method for calculation of the LQG ‘trade-off’ curves for performance assessment. The trade-off curve provides the optimal performance limit in terms of the best achievable input and output variances. Three possible scenarios for LQG control design in this supervisory-regulatory structure are discussed in the paper. The problem formulations are presented in the subspace framework to directly derive the control law and LQG trade-off curve without need of the conventional parametric models. A simulation example is provided to demonstrate the proposed method.     

An evaluation of the dynamical performance of composite slabs

The competitive trends of the world market have long been forcing structural engineers to develop minimum weight and labour cost solutions. A direct consequence of this new design trend is a considerable increase in problems related to unwanted floor vibrations. This phenomenon is very frequent in a wide range of structures subjected to rhythmic dynamical load actions. These load actions are generally caused by human rhythmic activities such as: musical and or sporting events, dance or even gymnastics. The main objective of this paper is to investigate the structural behaviour of commonly used composite floors subjected to rhythmic dynamical load actions identifying the occurrence of unwanted vibrations that could cause human discomfort or, in extreme cases, structural failure.     

On controlling prioritized discrete event systems with real-time constraints

We study a class of prioritized Discrete Event Systems (DESs) that involve the control of resources allocated to tasks under real-time constraints. Our work is motivated by applications in communication systems, computing systems, and manufacturing systems where the objective is to minimize energy consumption while guaranteeing that task deadlines are always met. In the off-line setting, we discover several structural properties of the optimal sample path of such DESs. Using the structural properties, we also propose a greedy algorithm which is shown numerically near optimal. For on-line control, we design a Receding Horizon (RH) controller. Using worst-case estimation, the RH control is able to guarantee feasibility (when the off-line problem is feasible) and achieve good performance.     

Combined design of structures and controllers for optimal maneuverability

This paper treats the problem of the combined design of structure/control systems for achieving optimal maneuverability. A maneuverability index which directly reflects the time required to perform a given maneuver or set of maneuvers is introduced. By designing the flexible appendages of a spacecraft, its maneuverability is optimized under the constraints of structural properties, and of the postmaneuver spill-over being within a specified bound. The spillover reduction is achieved by making use of an appropriate control design model. The distributed parameter design problem is approached using assumed shape functions and finite element analysis with dynamic reduction. Characteristics of the problem and problem solving procedures have been investigated. Adaptive approximate design methods have been developed to overcome computational difficulties. It is shown that the global optimal design may be obtained by tuning the natural frequencies of the spacecraft to satisfy specific constraints. We quantify the difference between a lower bound to the objective function associated with the original problem and the estimate obtained from the modified problem as the index for the adaptive refinement procedure. Numerical examples show that the results of the optimal design can provide substantial improvement.