Structural Optimization of Variable Section Slender Manipulator Based on Sensitivity Analysis Method

The computational cost of reliability analysis and optimization of medium/large structural systems is prohibitively high. One of the reasons for this situation is the use of inefficient methods, such as finite differences, for design sensitivity analysis. A significant increase in the efficiency of reliability computations is expected from the integration of reliability methods with the discrete and continuum methods of design sensitivity analysis. So far, only the discrete method has been used in the so-called stochastic finite element method. Integration of reliability computations with the continuum method of design sensitivity analysis is proposed in this paper as a new, powerful approach to the probabilistic design of large structural systems. Basic formulations and solution methods of reliability analysis, design sensitivity analysis of reliability indices, reliability-based optimization, and multiobjective reliability-based optimization are reviewed with focus on the sensitivity informatio...

Sensitivity analysis and optimization of truss/beam components of arbitrary cross-section—I. Axial stresses

The objective of this study is to examine two analytical methods for the design sensitivity analysis of optimal control problems and to develop the analyses necessary for the application of the methods to thermal systems. The two methods are the direct differentiation method and the adjoint variable method. Results for these methods are compared with those obtained using central finite difference approximations for design sensitivity analysis. The adjoint variable method has the potential to reduce significantly computational times for design sensitivity analysis while sacrificing only a small amount of accuracy. As the number of functional requiring design sensitivity analysis increases, however, the adjoint variable method becomes less attractive and the direct differentiation method becomes more attractive.

The author’s method of design sensitivity analysis of nonlinear coincident buckling load factors and corresponding optimization method of finite dimensional elastic structures are shown to be applicable to a structure with moderately large number of degrees of freedom. The sensitivity formulations are written in general form for coincident buckling load factors including limit points and bifurcation points. Optimum designs are found for a spherical latticed dome subjected to a concentrated load and distributed loads, respectively. The results are compared with those by linear eigenvalue formulation. An approximate optimal solution against nonlinear buckling can be obtained by only scaling the solution under linear eigenvalue formulation even for the case where the effect of prebuckling deformation is very large. It is shown that the proposed method is practically applicable to optimum design with coincident critical points especially for the case of hill-top branching where bifurcation points are located at the limit point. In this case, imperfection sensitivity is not enhanced as a result of optimization. The reduction of maximum load factor due to a minor imperfection is shown to be in the same order as that to a major imperfection. Therefore symmetric imperfection as well as asymmetric imperfection should be considered in estimating the maximum loads.

The optimization of the large structure with the layout of stiffener is considered by a new calculation method in this study. Many number of stiffener are attached to large structures. Optimization of the large structures with design variables of plate thickness and shape of stiffener is performed. However, in order to obtain a better optimal solution, the optimization of the structure with design variable of number of stiffener and allocation of stiffener is required. But, the optimization of structure with design variable of the number of stiffener and allocation of stiffener is not performed. There are two problems. The first problem is the FEM model. FEM models need some nodes at allocation of stiffener as a characteristic of FEM. When number of stiffener and allocation of stiffener are changed by the process of the optimization of the structure, number of nodes and allocation of nodes of FEM model is also changed. Therefore, in order to ensure consistency of mesh, it is necessary to remake FEM model. In order to optimize structural, it is necessary to examine many propositions for design. However it is difficult to create and analyze the proposition for design of many numbers in restricted time. The second problem is the optimization method. When the number and allocate of stiffeners are changed, the stricture is modified and the number of design variables is changed. The optimization problem with changed number of design variables cannot be optimized by standard optimization methods. The methods of solving these problems are examined.

During the last 20 years, structural optimization has become one of the most important topics of engineering applications. Design optimization of structure has been an interesting area of research in the field of engineering design for its ability to short the design cycle and to enhance product quality. Significant research activity has occurred in the area of structural optimization in the last decade. Especially for topology optimization of structure, many new theoretical, algorithmic, and computational contributions have resulted by researchers and engineers. Topology optimization is a powerful tool for global and multi-scale design of macrostructures, microstructures, and the cell of prescribed composite materials. The population based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems in engineering during the last two decades. Evolutionary computation is the study of computational systems which use ideas and get inspiration from natural evolution and adaptation [1]. The thinking has wide application in various engineering fields, such as computer science, artificial intelligence, operations research. Genetic algorithm is another kind of bio-inspired optimization method and it is playing an increasingly important role in studies of complex adaptive systems. Its application ranges from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices and structures, such as aircraft turbines and integrated circuits [2]. Optimization of structures can be classified into three categories: sizing, shaping, and topology optimization. In the topology optimization, it is concerned with the structure members and connectivity between members. In general, it is easily represented by discrete variables rather than by those used for continuous optimization problems. Topology optimization is the most difficult and complex among three categories and it is special useful in developing innovative conceptual designs. Structural optimization, in particular the topology optimization, has been identified as one of the most challenging tasks in structural design. Various techniques and approaches have been established during the last two decades. Topology optimization usually referred to as layout optimization or general shape optimization [3]. It lets engineers get the optimal topology of structure or new configurations during product design phase, as they are implementing the design of the size

Using the bond-based peridynamics and the parallel computation with binary decomposition, an adjoint shape design sensitivity analysis(DSA) method is developed for the dynamic crack propagation problems. The peridynamics includes the successive branching of cracks and employs the explicit scheme of time integration. The adjoint variable method is generally not suitable for path-dependent problems but employed since the path of response analysis is readily available. The accuracy of analytical design sensitivity is verified by comparing it with the finite difference one. The finite difference method is susceptible to the amount of design perturbations and could result in inaccurate design sensitivity for highly nonlinear peridynamics problems with respect to the design. It turns out that C1-continuous volume fraction is necessary for the accurate evaluation of shape design sensitivity in peridynamic discretization.

ACOMPUTATIONAL method for design sensitivity analysis of an eigenvalue and an eigenvector of a beam under nonlinear forced vibration is presented in this paper. The nonlinear vibration problem is only analyzed once in the proposed method. The geometric nonlinearity of concern results from the large deflection of a beam. The finite element system equation for nonlinear vibration is symmetric. However, it is found that the equation for computing the design sensitivity of an eigenvector is linear and unsymmetric. A numerical example is included to validate the proposed computational procedure. Contents The nonlinear vibrations studied herein refer to the periodic (though not necessarily harmonic) and stable motions of a nonlinear system. Recently, Hou and Yuan1 addressed the design sensitivity analysis of eigenvalues and eigenvectors of a beam under nonlinear free vibration. In that paper, the longitudinal inertia was not considered in the nonlinear vibration formulation, so that the problem could be expressed in terms of the lateral deflection alone. In the present work the design sensitivity analysis has been extended successfully to a nonlinear forced vibration problem whose formulation includes the in-plane inertia and displacement. The variational formulation2 for the nonlinear forced vibrations of beams under harmonic excitation is given as

Design sensitivity analysis (DSA) and topology design optimization methods forpiezoelectric resonators are developed. The governing equations for piezoelectric vibrationproblems are the Cauchy’s equation of motion and the charge equation of electrostatics. AMindlin plate theory using higher-order interpolations along the thickness direction that iseffective for the thickness-shear vibration analysis of piezoelectric resonators is used. Anoptimal design problem is formulated to maximize the electromechanical coupling strengthat the mode of interest. Necessary design gradients for eigenvalue problems are computedvery efficiently and accurately using an analytical DSA method with an eigenvectorexpansion concept. A robust mode-tracking method based on thickness-shear strain energyis proposed to precisely identify the thickness-shear mode at high frequencies.Through demonstrative numerical examples, the DSA method developed is verifiedto show excellent efficiency and agreement compared with the finite differencemethod. It is observed that the frequencies are almost invariant even though the sizeand shape of the crystal varies significantly. However, it is observed that theoptimal topology is sensitive to the aspect ratio even if the thicknesses are thesame.

A state space design sensitivity analysis and optimization method is presented in which problems of optimal design of machines are formulated in a setting that allows treatment of general design objectives and constraints. Synthesis of machines to perform both kinematic and kinetic functions is considered. A Cartesian coordinate formulation is employed for position, velocity, acceleration, and force analysis. An adjoint variable technique is employed to compute derivatives with respect to design of general cost and constraint functions that involve kinematic, force, and design variables. Linearization (or sequential quadratic programming) and gradient projection optimization algorithms are employed, using the design sensitivity analysis method developed, for design optimization. Four optimal design problems are solved to demonstrate use of the method.

Design sensitivity analysis and optimization for nonlinear buckling of finite-dimensional elastic conservative structures

Explicit and implicit methods for design sensitivity analysis of nonlinear structures subjected to transient dynamic loads are described. The direct differentiation method is used to calculate the sensitivities. Elastic and elasto-plastic problems undergoing large deformation are treated in the formulation. The explicit method is quite straightforward to implement for analysis as well as design sensitivity analysis: knowing all the quantities at time t, one updates the quantities for the next time point without solution of any linear system of equations, or any iterations. For the implicit method, the effective stiffness matrix for the sensitivity equation is different from that for the analysis phase due to inclusion of large deformation in the formulation. A numerical procedure to integrate the equation is proposed which uses the symmetric effective stiffness matrix from the analysis phase. Although the sensitivity analysis problem is linear, the procedure requires iterations for sensitivity calculations at each time step, as for the analysis phase. The implicit method is implemented using the pre-conditioned conjugate gradient iterative solution scheme. Numerical results for sensitivities indicate the implicit method to be more accurate than the explicit method for transient elastoplastic problems. However, the explicit method is substantially more efficient than the implicit method.

We propose an extension of the adjoint variable method for design sensitivity analysis to problems involving lossy materials. We first extend a recently developed discrete algorithm, which was originally applied to loss-free problems. It requires the solution of a stepwise perturbed structure that is available only approximately. Then, we enhance this algorithm by proposing a semi-analytical approach. The approach requires the solution of the unperturbed structure, which is readily available. It employs the analytical dependence of the system matrix on the material properties of the structure. All responses and their sensitivities are obtained through two system analyses. We consider applications with a frequency-domain solver based on the transmission line method (FDTLM).

Sensitivity analysis of eigenmodes and dynamic responses for intelligent structures

Isogeometric configuration design sensitivity analysis of geometrically exact shear-deformable beam structures