Shape design optimization of initial stressed bimetal composite structures for controlling vibrational eigenvalues

Abstract

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 H¹ 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.