An effective free vibration optimization procedure in combination with the isogeometric approach (IGA), particle swarm optimization (PSO) and an integrated global and local parameterization is presented. The natural frequency of functionally graded (FG) plates is calculated by the IGA based on the Bézier extraction of non-uniform rational B-splines (NURBS) with the cubic NURBS basis function. The material composition is assumed to vary only in the thickness direction, and the volumetric fraction is described by the NURBS basis function in light of the superior properties of NURBS curves. The volume fractions of the control points are then optimized by the PSO. In most of the previous work, the control points for the volume fraction are usually equally spaced, which is incapable of identifying the optimal location of the graded zones in most cases. To overcome this bottleneck, a novel local refinement strategy is proposed. The reliability and effectiveness of the proposed approach are demonstrated through several numerical examples. It is interesting to observe that the optimal results are sandwich or laminate plates, and few parameters are involved in the integrated global and local parameterization.

In this paper, the singular boundary method (SBM) in conjunction with the exponential window method (EWM) is firstly extended to simulate the transient dynamic response of two-dimensional saturated soil. The frequency-domain (Fourier space) governing equations of Biot theory is solved by the SBM with a linear combination of the fundamental solutions. In order to avoid the perplexing fictitious boundary in the method of fundamental solution (MFS), the SBM places the source point on the physical boundary and eliminates the source singularity of the fundamental solution via the origin intensity factors (OIFs). The EWM is carried out for the inverse Fourier transform, which transforms the frequency-domain solutions into the time-domain solutions. The accuracy and feasibility of the SBM-EWM are verified by three numerical examples. The numerical comparison between the MFS and SBM indicates that the SBM takes a quarter of the time taken by the MFS.