The symmetric interior penalty discontinuous Galerkin finite element method is presented for the numerical discretization of the second-order wave equation. The resulting stiffness matrix is symmetric positive definite and the mass matrix is essentially diagonal; hence, the method is inherently parallel and leads to fully explicit time integration when coupled with an explicit timestepping sche...

This paper presents an experimental and numerical study of unidirectional carbon fiber composites with a silicone matrix, loaded transversally to the fibers. The experiments show nonlinear behavior with significant strain softening under cyclic loading. The numerical study uses a plane-strain finite element continuum model of the composite material in which the fiber distribution is based on ex...

Isogeometric Analysis (IGA) was introduced by Hughes et al. in 2005 [1] as a new method to bridge the gap between the geometry description and numerical analysis. Similar to the finite element approach, the IGA concept to solve a partial differential equation leads to a (linear) system of equations. The condition number of the coefficient matrix is a crucial factor for the stability of the syst...

In this paper, a procedure has been presented to develop fragility curves of structures equipped with optimal variable damping or stiffness semi-active tuned mass dampers (SATMDs). To determine proper variable damping or stiffness of semi-active devices in each time step, instantaneous optimal control algorithm with clipped control concept has been used. Optimal SATMDs have been designed based ...

In this study,SGBEM Voronoi Cells (SVCs), with each cell representing a grain of the material at the micro-level, are developed for direct micromechanical numerical modeling of heterogeneous composites. Each SVC can consist of either a (each with a different) homogenous isotropic matrix, and can include micro-inhomogeneities such as inclusions, voids of a different material, and cracks. These i...

Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...

We study the dispersion and dissipation of the numerical scheme obtained by taking a weighted averaging of the consistent (finite element) mass matrix and lumped (spectral element) mass matrix for the small wavenumber limit. We find and prove that for the optimum blending the resulting scheme (a) provides 2p+4 order accuracy for p-th order method (two orders more accurate compared with finite a...

In this paper, a discontinuity in beams whose intensity is adjusted by the spring stiffness factor is modeled using a torsional spring. Adapting two analyses in strong and weak forms for discontinuous beams, the improved governing differential equations and the modified stiffness matrix are derived respectively. In the strong form, two different solution methods have been presented to make an a...

This study presents a fast and exact computational method for crack propagation which is based on the extended finite element method (X-FEM). It is well known that the X-FEM has been developed to be an important numerical method for crack propagation. However, there are still some limitations on the computational cost due to the requirements of very refined meshes and very small iteration step ...