Search results for "Boundary problem"

Infinitely many solutions for a mixed boundary value problem

2010

The existence of infinitely many solutions for a mixed boundary value problem is established. The approach is based on variational methods.

Wick Theorem for General Initial States

2012

We present a compact and simplified proof of a generalized Wick theorem to calculate the Green's function of bosonic and fermionic systems in an arbitrary initial state. It is shown that the decomposition of the non-interacting $n$-particle Green's function is equivalent to solving a boundary problem for the Martin-Schwinger hierarchy; for non-correlated initial states a one-line proof of the standard Wick theorem is given. Our result leads to new self-energy diagrams and an elegant relation with those of the imaginary-time formalism is derived. The theorem is easy to use and can be combined with any ground-state numerical technique to calculate time-dependent properties.

Frictionless contact-detachment analysis: iterative linear complementarity and quadratic programming approaches.

2012

The object of the paper concerns a consistent formulation of the classical Signorini’s theory regarding the frictionless contact problem between two elastic bodies in the hypothesis of small displacements and strains. The employment of the symmetric Galerkin boundary element method, based on boundary discrete quantities, makes it possible to distinguish two different boundary types, one in contact as the zone of potential detachment, called the real boundary, the other detached as the zone of potential contact, called the virtual boundary. The contact-detachment problem is decomposed into two sub-problems: one is purely elastic, the other regards the contact condition. Following this method…

Analytical Refinement of Sandwich Plate Bending Problem Considering Local Effects-I

1999

Analytic expressions for local flexural characteristics and stresses of sandwich panels under loading by point forces have been found. A discrete-layer model for bending of a three-layer panel with a soft filler is proposed. Contractility of a normal in the model is deduced in terms of a difference between deflections of face layers. The accountability of transverse shear in the filler and the sheets is deduced on piecewise rotation of the normal. Equations of the model having four degrees of displacement freedom are of twelfth order. The specific features of the stress from point forces in cylindrical bending are considered using the operational Laplace method with the generalized Dirac f…

A Variational Approach to Boundary Element Methods

1988

A new method for creating sparse design velocity fields

2006

We present a novel method for the computation of mesh node sensitivities with respect to the boundary node movement. The sensitivity field is sparse in a sense that movement of each boundary node affects only given amount of inner mesh nodes, which can result in considerable savings in the storage space. The method needs minimal control from the user, and it does not place any restrictions (such as block structure) on the mesh. Use of the method is demonstrated with a shape optimization problem using CAD-free parametrization. A solution to the classical die-swell free boundary problem by coupling the boundary node locations with the state variables is also presented. In that case, sparsity …

A Boundary Control Approach to an Optimal Shape Design Problem

1989

Abstract We consider the problem of controlling the coincidence set in connection with an obstacle problem. We shall transform the obtained optimal shape design problem into a boundary control problem with Dirichlet boundary conditions.

Boundary discretization based on the residual energy using the SGBEM

2007

Abstract The paper has as objective the estimation of the error in the structural analysis performed by using the displacement approach of the Symmetric Galerkin Boundary Element Method (SGBEM) and suggests a strategy able to reduce this error through an appropriate change of the boundary discretization. The body, characterized by a domain Ω and a boundary Γ−, is embedded inside a complementary unlimited domain Ω∞⧹Ω bounded by a boundary Γ+. In such new condition it is possible to perform a separate valuation of the strain energies in the two subdomains through the computation of the work, defined generalized, obtained as the product among nodal and weighted quantities on the actual boundar…

Types of solutions and multiplicity results for two-point nonlinear boundary value problems

2005

Abstract Two-point boundary value problems for the second-order ordinary nonlinear differential equations are considered. If the respective nonlinear equation can be reduced to a quasi-linear one with a non-resonant linear part and both equations are equivalent in some domain D , and if solutions of the quasi-linear problem lie in D , then the original problem has a solution. We then say that the original problem allows for quasilinearization. We show that a quasi-linear problem has a solution of definite type which corresponds to the type of the linear part. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions.

A nonlocal problem arising from heat radiation on non-convex surfaces

1997

We consider both stationary and time-dependent heat equations for a non-convex body or a collection of disjoint conducting bodies with Stefan-Boltzmann radiation conditions on the surface. The main novelty of the resulting problem is the non-locality of the boundary condition due to self-illuminating radiation on the surface. Moreover, the problem is nonlinear and in the general case also non-coercive. We show that the non-local boundary value problem admits a maximum principle. Hence, we can prove the existence of a weak solution assuming the existence of upper and lower solutions. This result is then applied to prove existence under some hypotheses that guarantee the existence of sub- and…