Dynamic von-Kármán plate models consist of three coupled non-linear, time-dependent partial differential equations. These equations have been recently solved numerically [Kirby, R., Yosibash, Z., 2004. Solution of von-Kármán dynamic non-linear plate equations using a pseudo-spectral method. Comp. Meth. Appl. Mech. Eng. 193 (6–8) 575–599 and Yosibash, Z., Kirby, R., Gottlieb, D., 2004. Pseudo-sp...

An implicit integration strategy was developed and implemented for use with the material point method (MPM). An incremental-iterative solution strategy was developed around Newton’s method to solve the equations of motion with Newmark integration to update the kinematic variables. Test problems directly compared the implicit MPM solutions with those obtained using an explicit MPM code and impli...

We present a time-dependent finite element model of the human knee joint of full 3D geometric complexity together with advanced numerical algorithms needed for its simulation. The model comprises bones, cartilage and the major ligaments, while patella and menisci are still missing. Bones are modeled by linear elastic materials, cartilage by linear viscoelastic materials, and ligaments by onedim...

Seismic tomography is a technique to determine the material properties of the Earth’s subsurface based on the observation of seismograms. This can be stated as a PDE-constrained optimization problem governed by the elastic wave equation. We present a semismooth Newton-PCG method with a trust-region globalization for full-waveform seismic inversion that uses a MoreauYosida regularization to hand...

A novel enriched finite element method (EFEM) was employed to analyze the transient wave propagation problems. In present method, traditional approximation by employing appropriate interpolation covers. We mathematically and numerically showed that EFEM possessed important monotonic convergence property with decrease of used time steps for problems when unconditional stable Newmark integration ...