Three-dimensional periodic materials as seismic base isolator for nuclear infrastructure

PERIODIC SOLUTIONS OF CERTAIN THREE DIMENSIONAL AUTONOMOUS SYSTEMS

There has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. The popular Poincare-Bendixon theorem applies well to the former but not the latter (see [2] and [3]). We give a necessary condition for the existence of periodic solutions for the third order autonomous system...

Materials informatics as a computational infrastructure for materials discovery

One of the critical barriers in transitioning new materials development into engineering practice is the uncertainty associated with the data that is used in the materials design process. While constitutive modeling strategies still form the foundations for computational materials design, uncertainty and incomplete information still pervade. Often the available data space is limited, and the ch...

Three-Dimensional Interfacial Green’s Function for Exponentially Graded Transversely Isotropic Bi-Materials

By virtue of a complete set of two displacement potentials, an analytical derivation of the elastostatic Green’s functions of an exponentially graded transversely isotropic bi-material full-space was presented. Three-dimensional point-load Green’s functions for stresses and displacements were given in line-integral representations. The formulation included a complete set of transformed stress-p...

Frozen Gaussian approximation for three-dimensional seismic wave propagation

periodic solutions of certain three dimensional autonomous systems

there has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. the popular poincare-bendixon theorem applies well to the former but not the latter (see [2] and [3]). we give a necessary condition for the existence of periodic solutions for the third order autonomous systems, t...