Search results for "Mathematical analysis"

Symmetric boundary element method versus finite element method

2002

The paper examines the effectiveness of the symmetric boundary element formulation when the continuum body is subdivided into large elements called macro-elements. The approach proposed combines a strong reduction of variables with an elastic solution close to the real response. Indeed, if the displacement method is used, this approach permits one to determine for every macro-element a relationship connecting the weighted traction vector defined on the sides of the interface boundary with the node displacement vector of the same boundary and with the external action vector. Such a strategy is very similar to that followed through the finite element method, but with the advantages of having …

CVBEM solution for De Saint-Venant orthotropic beams under coupled bending and torsion

2014

The aim of this paper is to provide a solution for the coupled flexure–torsion De Saint Venant problem for orthotropic beams taking full advantage of the complex variable boundary element method (CVBEM) properly extended using a complex potential function whose real and imaginary parts are related to the shear stress components, the orthotropic ratio and the Poisson coefficients. The proposed method returns the complete stress field and the unitary twist rotation of the cross section at once by performing only line integrals. Numerical applications have been reported to show the validity and the efficiency of the proposed modified CVBEM to handle shear stress problems in the presence of ort…

Complex Potential Function in Elasticity Theory: shear and torsion solution through line integrals

2012

Aim of this paper is to introduce a basis formulation framed into complex analysis valid to solve shear and torsion problems. Solution, in terms of a complex function related to the complete tangential stress field, may be evaluated performing line integrals only. This basis formulation framed into elasticity problems may be a useful support for a boundary method to verify the accuracy of an approximation of function solution. The numerical applications stress the latter point and show the validity of these formulas since exact solutions may be reached for sections where the exact solution is known.

Some observations on the regularizing field for gradient damage models

2000

Gradient enhanced material models can potentially preserve well-posedness of incremental boundary value problems also after the onset of strain softening. Gradient dependent constitutive relations are rooted in the assumption that some scalar or tensor field, which appears in the yield function, has to be enriched by adding a term involving its second-order gradient field. For gradient-dependent plasticity this term is universally accepted to be the equivalent plastic strain. For gradient-dependent damage models different choices have been presented in the literature. They all possess the desired regularization of the solution, but they are not identical as regards the structural response. …

Lagrangian finite element modelling of dam–fluid interaction: Accurate absorbing boundary conditions

2007

The dynamic dam-fluid interaction is considered via a Lagrangian approach, based on a fluid finite element (FE) model under the assumption of small displacement and inviscid fluid. The fluid domain is discretized by enhanced displacement-based finite elements, which can be considered an evolution of those derived from the pioneering works of Bathe and Hahn [Bathe KJ, Hahn WF. On transient analysis of fluid-structure system. Comp Struct 1979;10:383-93] and of Wilson and Khalvati [Wilson EL, Khalvati M. Finite element for the dynamic analysis of fluid-solid system. Int J Numer Methods Eng 1983;19:1657-68]. The irrotational condition for inviscid fluids is imposed by the penalty method and con…

On the translation of the three fundamental problems of elastic equilibrium of anisotropic bodies into systems of Fredholm first kind integral equati…

1972

Form defect influence on the shrinkage fit characteristics

1998

Abstract Today, manufacturing products must meet more and more severe specifications. The different parts composing the product often necessitate high dimensional precision, which increases the difficulties for a large series production. Then it it necessary to optimize dimensioning of the different components in an economic context. In the case of small dimensional fits, there is an influence of the micro-geometry (form of defect, roughness) and time of the process on the geometrical characteristics of the assembly. At the time of conception, it is necessary to obtain a good specification that relates the product functionalities with the best cost. The objective study of this is to simulat…

CVBEM application to a novel potential function providing stress field and twist rotation at once

2013

AbstractIn this paper, complex variable boundary element method (CVBEM) is used for the solution of de Saint-Venant’s torsion problem in homogenous isotropic elastic beams with a generic cross section, considering a complex potential function related to the stress field. Generally, CVBEM, when used for torsion problems, leads to evaluation of the stress field divided by the twist rotation. The latter has been evaluated by performing a domain integral. In this paper, taking advantage of the aforementioned potential function, it is possible, by applying CVBEM, to evaluate the complete stress distribution and the twist rotation of the cross section and the torsional stiffness factor, performin…

Solution strategies for 1D elastic continuum with long-range interactions: Smooth and fractional decay

2010

Abstract An elastic continuum model with long-range forces is addressed in this study within the context of approximate analytical methods. Such a model stems from a mechanically-based approach to non-local theory where long-range central forces are introduced between non-adjacent volume elements. Specifically, long-range forces depend on the relative displacement, on the volume product between interacting elements and they are proportional to a proper, material-dependent, distance-decaying function. Smooth-decay functions lead to integro-differential governing equations whereas hypersingular, fractional-decay functions lead to a fractional differential governing equation of Marchaud type. …

The ∞-Eigenvalue Problem

1999

. The Euler‐Lagrange equation of the nonlinear Rayleigh quotient \( \left(\int_{\Omega}|\nabla u|^{p}\,dx\right) \bigg/ \left(\int_{\Omega}|u|^{p}\,dx\right)\) is \( -\div\left( |\nabla u|^{p-2}\nabla u \right)= \Lambda_{p}^{p} |u |^{p-2}u,\) where \(\Lambda_{p}^{p}\) is the minimum value of the quotient. The limit as \(p\to\infty\) of these equations is found to be \(\max \left\{ \Lambda_{\infty}-\frac{|\nabla u(x)|}{u(x)},\ \ \Delta_{\infty}u(x)\right\}=0,\) where the constant \(\Lambda_{\infty}=\lim_{p\to\infty}\Lambda_{p}\) is the reciprocal of the maximum of the distance to the boundary of the domain Ω.