Topics Direct Approach for Discrete Systems Strong and Weak Forms for One-Dimensional Problems Second order boundary value problems (1D) Scalar field problems: heat conduction, advection-diffusion Triangular elements Computer implementation Isoparametric elements Numerical integration Vector field problems: elasticity equations Beam elements Eigenvalue problems Time dependent problems Special t...

In this paper a composite plate with similar unidirectional fibers is considered. Assuming orthotropic structure, theory of elasticity is used for investigating the stress concentration. Also, complex variable functions are utilized for solving the plane stress problems. Then the effective characteristics of this plate are studied numerically by using ANSYS software. In this research a volume e...

Non-linear elasticity theory may be used to calculate the coordinates of a deformed body when the coordinates of the undeformed, stress-free body are known. In some situations, such as one of the steps in the location of tumours in a breast, the coordinates of the deformed body are known and the coordinates of the undeformed body are to be calculated, i.e. we require the solution of the inverse...

We present an algebraic multigrid (AMG) method for the efficient solution of linear (block-)systems stemming from a discretization of a system of partial differential equations (PDEs). It generalizes the classical AMG approach for scalar problems to systems of PDEs in a natural blockwise fashion. We apply this approach to linear elasticity and show that the block-interpolation, described in thi...

We consider the equations of linear homogeneous anisotropic elasticity admitting the possibility that the material is internally constrained, and formulate a simple necessary and sufficient condition for the fundamental boundary value problems to be well-posed. For materials fulfilling the condition, we establish continuous dependence of the displacement and stress on the elastic moduli and ell...

In the classical approach to elasticity problems, the components of the displacement field are the primary unknowns. In an “intrinsic” approach, new unknowns with more physical or geometrical meanings, such as a strain tensor field or a rotation field for instance, are instead taken as the primary unknowns. We survey here recent progress about the mathematical analysis of such methods applied t...

An energy-based, phase field model is developed for the coupling of two incompressible, immiscible complex fluid phases, in particular a nematic liquid crystal phase in a viscous fluid phase. The model consists of a system of coupled nonlinear partial differential equations for conservation of mass and momentum, phase transport, and interfacial boundary conditions. An efficient and easy-to-impl...

Abstract. Balancing Neumann-Neumann methods are extented to mixed formulations of the linear elasticity system with discontinuous coeÆcients, discretized with mixed nite or spectral elements with discontinuous pressures. These domain decomposition methods implicitly eliminate the degrees of freedom associated with the interior of each subdomain and solve iteratively the resulting saddle point S...

In this work, the robustness of the fluid-structure interaction simulation with a nearly incompressible elasticity model from our previous work [Partitioned solvers for the fluid-structure interaction problems with a nearly incompressible elasticity model, Comput Visual Sci, 14:227-247, 2012] is improved. At each time step of the FSI simulation, using properly chosen elementwise stabilization p...

This paper estimates the income elasticity of health care expenditures using annual data on health spending by state in the U.S. from 1966-2009. Panel stationarity tests incorporating structural breaks in the levels and trends in Health Care Expenditures and Disposable Personal Income yield inconsistent results, with stationarity rejected for HCE but not for DPI. Regression results using levels...