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By combining different material properties of two metals, bimetals have been widely designed and manufactured as parts or accessories in automobile, aircraft, marine engineering for providing specific requirements. Hence, shape design optimization of bimetal composite structures performs an important role for obtaining their best mechanical or physical behaviors. In addition, initial stress of bimetal composite structures generated during the manufacturing or assembling process cannot be ignored. In this study, to control the vibrational eigenvalues of bimetals, we develop a shape design optimization method to obtain the optimal shapes of initial stressed bimetal composite structures. In the formulation of the design problem, we use minus vibrational eigenvalues multiplied by weighting coefficients as the objective function. Hence, the present work can treat vibrational eigenvalue maximization or vibrational eigenvalues' gap maximization by adjusting the weight coefficients. We minimize the objective function subjected to the governing equations of structural analysis for generating the initial stress and vibrational eigenvalue analysis considering the initial stress. We also consider the volume constraint as the constraint condition. Then, we theoretically derive the shape gradient function based the method of Lagrange multiplier and the material derivative method, and use the derived shape gradient function to calculate the optimal shape variation based on the H 1 gradient method. At last, we construct the shape design optimization system for determining the optimal shapes of bimetal composite structures conveniently. From the optimal results of design examples, we confirm that the developed shape design optimization method has efficiency and validity for controlling vibrational eigenvalues of bimetal composite structures.
By combining different material properties of two metals, bimetals have been widely designed and manufactured as parts or accessories in automobile, aircraft, marine engineering for providing specific requirements. Hence, shape design optimization of bimetal composite structures performs an important role for obtaining their best mechanical or physical behaviors. In addition, initial stress of bimetal composite structures generated during the manufacturing or assembling process cannot be ignored. In this study, to control the vibrational eigenvalues of bimetals, we develop a shape design optimization method to obtain the optimal shapes of initial stressed bimetal composite structures. In the formulation of the design problem, we use minus vibrational eigenvalues multiplied by weighting coefficients as the objective function. Hence, the present work can treat vibrational eigenvalue maximization or vibrational eigenvalues' gap maximization by adjusting the weight coefficients. We minimize the objective function subjected to the governing equations of structural analysis for generating the initial stress and vibrational eigenvalue analysis considering the initial stress. We also consider the volume constraint as the constraint condition. Then, we theoretically derive the shape gradient function based the method of Lagrange multiplier and the material derivative method, and use the derived shape gradient function to calculate the optimal shape variation based on the H 1 gradient method. At last, we construct the shape design optimization system for determining the optimal shapes of bimetal composite structures conveniently. From the optimal results of design examples, we confirm that the developed shape design optimization method has efficiency and validity for controlling vibrational eigenvalues of bimetal composite structures.
The purpose of this paper is to construct a methodology which can produce a lightweight panel structure while being satisfied with more than one constraint by using some simple model. In this study, we chose a problem including bending stiffness and the 1 st order eigen frequency as constraints and volume minimization as objective function among basic performances which a vehicle requires. So far, we have been trying to solve the problem by using a method consisting of Fully Stressed Design (FSD) and Genetic Algorithm (GA). FSD is an optimization which evaluates only stiffness of a structure based on relationship between thickness and stress, while GA, a broad array method, can have various number of objective functions and constraints. Prior to this study, the authors found a process was effective that stresses on the elements were to be equalized in the 1st step by applying FSD that made an individual superior on static stiffness. In this study, proposed method, which includes a process of equalization on normalized stresses on eigen vibrations, are added to that of static stresses in the 1st step. In the 2nd step, GA is selected. GA conducts operations, such as select, crossing, and mutation repeatedly until this attains a final solution. As for the model, we chose a sandwich panel which is equipped with top and bottom plates and interlayer lattice stiffeners. The reason for this selection is that the sandwich panel is lightweight and superior to stiffness, dumping, and strength. As a result, the obtained model presents a lightweight structure while being satisfied with the requirements of both stiffness and eigen frequency. Moreover, the proposed method attains optimized results earlier than GA without using FSD.
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