Frame Shape Optimization Subject To Dynamics Constraints

Structure dynamic performance can be improved greatly by use of shape optimization. Most research deals with truss shape optimization. Little research has addressed for frame shape optimization. In this paper, the research work is performed for frame shape optimization with frequency constraints.The present paper deals with the problem of determining the optimal node position of linearly elastic space frames with imposed frequency constraints.Recently, an optimization algorithm called the generalized Evolutionary Shift Method is proposed for truss shape optimization while being subject to design constraints in statics and dynamics, respectively. On the basis of the sensitivity analysis, trusses are optimally designed for the prescribed purpose by the strategy of shifting. The method is simple and efficient. The main characteristic of the solution methodology is the use of the Evolutionary Shift method as an optimizer. This paper reports the development of a computer-based systematic method for the dynamic shape optimization of planar frame and three-dimensional frame.It is found that the complexity of frequency sensitivity calculation varies with the element type. When the element dimension increases, the derivative of state variable with respect to design parameters becomes difficultly deduced. To avoid the complicated deductive work in the frequency sensitivity analysis, the first difference is used to substitute for the first derivative of mass matrix and stiffness matrix with respect to node coordinates. Illustrative examples of optimal design of a planar tower and a space dome are presented.