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Fuzzy analysis can be used to model the uncertainties present in structures. In particular, the fuzzy finite element method can be used to find the response of structures (isotropic or composite) involving uncertainties. For the integrated structural control of a system, the design of a fuzzy optimal controller is explored. In the past few years, some researchers have tried to design a fuzzy optimal controller based on the Takagi and Sugeno model. In this work, a different (new) approach is proposed for the design of a controller in the context of fuzzy optimal control theory. In most practical applications, the structural and material parameters vary considerably and are subject to uncertainties, mainly due to the uncontrollable aspects associated with the manufacturing and assembly of composite materials. These uncertainties, in many cases, cannot be modeled probabilistically because the probability distributions of the uncertain parameters are not usually known. Also, in some situations, the parameters are known only in linguistic form. A fuzzy finite element approach has been developed for the analysis of structures with fuzzy parameters. Using the deterministic optimal control theory as a basis, a fuzzy optimal control theory is developed so that the controller can be used to act as either a regulator or a tracking system. The control of a planar truss is presented to demonstrate the feasibility and applicability of the methodology presented.

Although much attention has been focused on the development and applications of fuzzy optimization, multiobjective programming, and mixed-discrete optimization methods separately, fuzzy multiobjective optimization problems in mixed-discrete design space have not been addressed in the literature. It is mainly because of the lack of mature and robust theories of mixed-discrete and multiobjective optimization. In most practical applications, designers often encounter problems involving imprecise or fuzzy information, multiple objectives, and mixed-discrete design variables. A new method is presented in which the fuzzy A formulation and game theory techniques are combined with a mixed-discrete hybrid genetic algorithm for solving mixed-discrete fuzzy multiobjective programming problems. Three example problems, dealing with the optimal designs of a two-bar truss, a conical convective spine, and a 25-bar truss, demonstrate that the method can be flexibly and effectively applied to various kinds of engineering design problems to obtain more realistic and satisfactory results in an imprecise environment.

The modeling, analysis, and design of large and complex composite structures involve the use of the finite element approach. In most practical applications the structural and material parameters vary considerably and are subject to uncertainties, mainly because of the uncontrollable aspects associated with the manufacturing and assembly of composite materials. In many cases, the probabilistic methods cannot be applied because the probability distributions of the uncertain parameters are not usually known. Also, in some situations the parameters are known only in linguistic form. In this work, the uncertainties encountered in composite structures, which can be described in linguistic terms or in imprecise form, are modeled as fuzzy parameters. A fuzzy finite element analysis technique is developed for the analysis of laminated beams, involving fuzziness, possibly in the boundary conditions as well. The fuzzy beam element can undergo axial, bending, and transverse shear deformations. Using the basic concepts of the deterministic finite element theory, as well as fuzzy computations and fuzzy matrix operations, a fuzzy beam element is developed. The fuzzy beam element is used for the static and eigenvalue analysis of beams involving imprecise data and/or information. A numerical example is presented to demonstrate the feasibility and applicability of the methodology presented.

Fiber-reinforced composite materials have been used very widely and have emerged as a major class of structural materials in recent years. They are either used or being considered for use as substitutes for metals in many weight-critical components in aerospace and other industries. In most practical applications, the material parameters vary considerably and are subject to uncertainties, mainly due to the uncontrollable aspects associated with the manufacturing process. The probabilistic methods cannot be applied easily because the exact probability distributions of the uncertain parameters are not known. Also, in some situations, the parameters of a composite material are known only in linguistic form. Hence, fuzzy concepts are introduced to model the uncertainties encountered in composite materials, which may he described in uncertain terms or in imprecise/linguistic form as fuzzy parameters. When the basic fuzzy arithmetic computations, such as fuzzy addition, subtraction, multiplication, and division, and fuzzy square root and fuzzy trigonometry computations are used, different composite material mechanics expressions are explored, and the fuzzy analysis of fiber-reinforced composite material mechanics is presented. Numerical examples are given to demonstrate the feasibility and applicability of the approach. Other types of uncertainties, such as interval and probabilistic parameters, can also be accommodated with the approach.

The piezoelectric transducers embedded in structures offer distributed sensor and actuator architectures for structural control, a process that involves health monitoring and control of local structural degrees of freedom. The design steps demand sensor and actuator management schemes so that the response of a structural component in question is monitored and then tailored to the design requirements. Kalman's inverse theory is used to determine sensor and sensor-actuator combinations for optimal observers and controllers. The Riccati equations for each combination are derived to formulate the linear quadratic Gaussian theory for a reconfigurable architecture. An oscillator model with two inputs is considered to illustrate the underlying structural control principles.

A procedure is developed to allow the use of finite element method (FEM) in handling engineering systems in the presence of hybrid uncertainties characterized by design imprecision or stochastic uncertainty. This unified FEM scheme can be used to evaluate the impact of input uncertainties on output system response. The computational aspects of the procedure is illustrated by two numerical examples.

The use of fuzzy optimization techniques for the design of mechanical and structural systems is discussed. The technique relies on linear membership functions to solve the fuzzy mathematical programming problems involved in a decision-making process. To evaluate its reliability, this optimization approach is employed in the solution two design problems regarding truss construction. Results reveal that the sign of the membership satiation coefficient strongly affects the optimum designs of both sample specimens.