Search results for "Mixed boundary condition"

A NEW SYMMETRIC AND POSITIVE DEFINITE BOUNDARY ELEMENT FORMULATION FOR LATERAL VIBRATIONS OF PLATES

1997

Abstract A new symmetric and positive definite boundary element method in the time domain is presented for the dynamic analysis of thin elastic plates. The governing equations of the problem are obtained from a variational principle in which a hybrid modified functional is employed. The functional is expressed in terms of the domain and boundary basic variables in plate bending, assumed to be independent of each other. In the discretized model the boundary variables are expressed by nodal values, whereas the internal displacement field is modelled by a superposition of static fundamental solutions. The equations of motion are deduced from the functional stationarity conditions and they cons…

Parallel fictitious domain method for a non‐linear elliptic neumann boundary value problem

1999

Parallelization of the algebraic fictitious domain method is considered for solving Neumann boundary value problems with variable coefficients. The resulting method is applied to the parallel solution of the subsonic full potential flow problem which is linearized by the Newton method. Good scalability of the method is demonstrated on a Cray T3E distributed memory parallel computer using MPI in communication. Copyright © 1999 John Wiley & Sons, Ltd.

A boundary min-max principle as a tool for boundary element formulations

1991

Abstract A min-max principle for elastic solids, expressed in terms of the unknown boundary displacements and tractions, is presented. It is shown that its Euler-Lagrange equations coincide with the classical boundary integral equations for displacements and for tractions. This principle constitutes a suitable starting point for a symmetric sign-definite formulation of the boundary element method.

Multiplicity of solutions for two-point boundary value problems with asymptotically asymmetric nonlinearities

1996

Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System

2016

We consider the second order system x′′=f(x) with the Dirichlet boundary conditions x(0)=0=x(1), where the vector field f∈C1(Rn,Rn) is asymptotically linear and f(0)=0. We provide the existence and multiplicity results using the vector field rotation theory.

Multiplicity of Solutions for Second Order Two-Point Boundary Value Problems with Asymptotically Asymmetric Nonlinearities at Resonance

2007

Abstract Estimations of the number of solutions are given for various resonant cases of the boundary value problem 𝑥″ + 𝑔(𝑡, 𝑥) = 𝑓(𝑡, 𝑥, 𝑥′), 𝑥(𝑎) cos α – 𝑥′(𝑎) sin α = 0, 𝑥(𝑏) cos β – 𝑥′(𝑏) sin β = 0, where 𝑔(𝑡, 𝑥) is an asymptotically linear nonlinearity, and 𝑓 is a sublinear one. We assume that there exists at least one solution to the BVP.

Stress fields by the symmetric Galerkin boundary element method

2004

The paper examines the stress state of a body with the discretized boundary embedded in the infinite domain subjected to layered or double-layered actions, such as forces and displacement discontinuities on the boundary, and to internal actions, such as body forces and thermic variations, in the ambit of the symmetric Galerkin boundary element method (SGBEM). The stress distributions due to internal actions (body forces and thermic variations) were computed by transforming the volume integrals into boundary integrals. The aim of the paper is to show the tension state in Ω∞ as a response to all the actions acting in Ω when this analysis concerns the crossing of the discretized boundary, thu…

Two -methods to generate Bézier surfaces from the boundary

2009

Two methods to generate tensor-product Bezier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of @D^4x->=0 with prescribed boundary and adjacent to the boundary control points of a nxn Bezier surface. The second one is based on the nonhomogeneous biharmonic equation @D^2x->=p, where p could be understood as a vectorial load adapted to the C^1-boundary conditions.

Existence and Regularity for a Class of Nonlinear Hyperbolic Boundary Value Problems

2002

AbstractThe regularity of the solution of the telegraph system with nonlinear monotone boundary conditions is investigated by two methods. The first one is based on D'Alembert-type representation formulae for the solution. In the second method the telegraph system is reduced to a linear Cauchy problem with a locally Lipschitzian functional perturbation; then regularity results are established by appealing to the theory of linear semigroups.

Multiple solutions for a discrete boundary value problem involving the p-Laplacian.

2008

Multiple solutions for a discrete boundary value problem involving the p-Laplacian are established. Our approach is based on critical point theory.