Numerical methods for static shallow shells lying over an obstacle

Numerical Algorithms - In this paper, a finite element analysis to approximate the solution of an obstacle problem for a static shallow shell confined in a half space is presented. To begin with,...     

UPML formulation for truncating conductive media in curvilinear coordinates

This work presents a formulation based on UPML for truncating conductive media by using a local and non-orthogonal coordinate system to solve Maxwell’s equations by the FDTD method. The detailed procedure for obtaining the UPML equations for this case is shown and the complete equation set is provided.     

The obstacle problem for water tanks

In this paper we discuss the problem of computing and analyzing the static equilibrium of a nonrigid water tank. Specifically, we fix the amount of water contained in the tank, modelled as a membrane. In addition, there are rigid obstacles that constrain the deformation. This amounts to a nonconvex variational problem. We derive the optimality system and its interpretation in terms of equilibrium of forces. A second-order sensitivity analysis, allowing to compute derivatives of solutions and a second-order Taylor expansion of the cost function, is performed, in spite of the fact that the cost function is not twice differentiable. We also study the finite elements discretization, introduce a decomposition algorithm for the numerical computation of the solution, and display numerical results.     

The Keldys-Fichera obstacle problem

In this paper we consider a quasilinear obstacle problem with coefficients of higher growth orders and the Keldys-Fichera boundary condition. Research supported by the Fund of IMAS     

The regularization method for an obstacle problem

Summary. We give a relatively complete analysis for the regularization method, which is usually used in solving non-differentiable minimization problems. The model problem considered in the paper is an obstacle problem. In addition to the usual convergence result and a-priori error estimates, we provide a-posteriori error estimates which are highly desired for practical implementation of the regularization method. Received March 22, 1993 / Revised version received October 11, 1993     

The obstacle problem for an elastoplastic body

The obstacle problem for elastoplastic bodies is considered within the framework of general existence results for unilateral problems recently presented by Baiocchiet al. Two models of plasticity are considered: one is based on a displacement-plastic strain formulation and the second, a specialization of the first, is the standard Hencky model. Existence theorems are given for the Neumann problem for a body constrained to lie on or above the half-space {x³:x ³0}. For hardening materials the displacements are sought in the Sobolev spaceH ¹(, ³) while for perfectly plastic materials they are sought in BD(), the space of functions of bounded deformation. Conditions for the existence of solutions are given in terms of compatibility and safe load conditions on applied loads.This work was initiated while B. D. Reddy was on leave at the Istituto di Analisi Numerica del CNR, Pavia, Italy. The hospitality of that institution is gratefully acknowledged, as is the award of an FRD sabbatical grant. F. Tomarelli was partially supported by IAN and GNAFA of CNR, and by Ministero della Pubblica Istruzione.     

The obstacle problem for beams and plates

The numerical solution of the obstacle problem for beams and plates by means of variational inequalities and finite elements is examined. Algorithms for the solution of the discrete problem are discussed and particular attention is paid to different methods of approximating the constraint. The results of some numerical experiments for beams and plates are included.     

The obstacle problem for Monge Ampere equation

We consider the following obstacle problem for Monge-Ampere equation and discuss the regularity of the free boundary . We prove that is if f is bounded away from 0 and , and it is C ^1,1 if .Received: 4 February 2003, Accepted: 3 March 2004, Published online: 16 July 2004     

A difference scheme for the mixed boundary-value problem of strong bending of shallow shells

Translated from Issledovaniya po Prikladnoi Matematike, No. 5, pp. 32–52, 1976.     

The obstacle problem for quasilinear stochastic integral-partial differential equations

ABSTRACT

We prove the existence and uniqueness of solutions to a kind of quasilinear stochastic integral-partial differential equations with obstacles. Our method is based on the probabilistic interpretation of the solutions so that penalization method can be applied to a sequence of backward doubly stochastic differential equations with jumps. Relations between regular potentials and regular measures play an important role.     

Starshapedness in the obstacle problem

We establish the starshapedness (with respect to the origin) of coincidence set in the obstacle problem for second order elliptic equations.     

The stochastic obstacle problem for the harmonic oscillator with damping

We study the Kolmogorov equation associated with a second order stochastic variational inequality related to the harmonic oscillator.     

Temperature singularities for thin shallow shells and plates

We construct a fundamental solution of the equations of thermoelasticity of thin shallow isotropic shells of arbitrary Gaussian curvature. The solution is obtained as a series whose coefficients are definite integrals of a special function resembling the macdonald function in its properties. We find the temperature singularities for internal force factors. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 81–87.