Affiliations: Department of Civil and Structural Engineering, Aalto
University, Espoo, Finland | College of Civil and Architecture Engineering, Guangxi
University, Nanning, China | Department of Mechanical Engineering, Indiana
University-Purdue University Indianapolis, Indianapolis, IN, USA
Note: [] Corresponding author: Qimao Liu, Department of Civil and
Structural Engineering, Aalto University, Espoo, FI-00076 Aalto, Finland. Tel.:
+358 9 470 23701; Fax: +358 9 470 23758; E-mail: liuqimao2005@163.com
Abstract: This paper developed an effective optimization method, i.e.,
gradient-Hessian matrix-based method or second order method, of frame
structures subjected to the transient loads. An algorithm of first and second
derivatives of dynamic displacement and stress with respect to design variables
is formulated based on the Newmark method. The inequality time-dependent
constraint problem is converted into a sequence of appropriately formed
time-independent unconstrained problems using the integral interior point
penalty function method. The gradient and Hessian matrixes of the integral
interior point penalty functions are also computed. Then the Marquardt's method
is employed to solve unconstrained problems. The numerical results show that
the optimal design method proposed in this paper can obtain the local optimum
design of frame structures and sometimes is more efficient than the augmented
Lagrange multiplier method.
