Search results for "boundary"
showing 10 items of 1626 documents
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…
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…
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…
Bending stress fields in composite laminate beams by a boundary integral formulation
1999
Abstract The elasticity of a composite laminate under bending loads is approached through a boundary integral formulation and solved by the boundary element method. The integral equations governing the behaviour of each layer within the laminate, are deduced using the reciprocity theorem. Exact analytical singular solutions of the generalized orthotropic elasticity, i.e. the fundamental solutions of the problem, are employed as the kernels of the integral equation. The formulation does not make any assumption as to the nature of the elastic response and it allows consideration of general section geometries and stacking sequences. The solution is obtained through the enforcement of the inter…
Lower bounds for eigenvalues of a quadratic form relative to a positive quadratic form
1968
Abstract : A method is presented for the calculation of lower bounds to eigenvalues of operators that arise from variational problems for one quadratic form relative to a positive definite quadratic form. Eigenvalue problems of this kind occur, for example, in the theory of buckling of continuous linear elastic systems. The technique used is a modification of one introduced earlier, (1) sections II and IVB, for the determination of lower bounds to eigenvalues of semi-bounded self-adjoint operators. Other methods for the latter problem can be carried over without essential changes. The particular difficulty in the case we consider is that some operators which enter the calculation for the lo…
A thermodynamic approach to nonlocal plasticity and related variational principles
1999
Elastic-plastic rate-independent materials with isotropic hardening/softening of nonlocal nature are considered in the context of small displacements and strains. A suitable thermodynamic framework is envisaged as a basis of a nonlocal associative plasticity theory in which the plastic yielding laws comply with a (nonlocal) maximum intrinsic dissipation theorem. Additionally, the rate response problem for a (continuous) set of (macroscopic) material particles, subjected to a given total strain rate field, is discussed and shown to be characterized by a minimum principle in terms of plastic coefficient. This coefficient and the relevant continuum tangent stiffness matrix are shown to admit, …
Dynamic response of beams excited by moving oscillators: Approximate analytical solutions for general boundary conditions
2023
In this paper, the dynamic response of an Euler-Bernoulli beam with general boundary conditions (BCs) and subject to a moving oscillator is examined. Notably, novel approximate closed-form expressions are determined for the vertical responses of both the beam and the moving oscillator, specifically considering the effect of damping in these systems, commonly omitted in standard approaches in the literature. In this regard, a modal superposition procedure is adopted and combined with an appropriate expansion-based approach of the dynamic response of the system, which naturally arises considering the oscillator-beam mass ratio to be reasonably small. Further, general boundary conditions are t…
Direct stiffness matrices of BEs in the Galerkin BEM formulation
2001
Abstract In the analysis of an elastic two-dimensional solid body by means of the Symmetric Galerkin Boundary Element Method (SGBEM), difficulties arise in the computation of some terms of the solving system coefficients. In fact these coefficients are expressed as double integrals with singularities of order 1/ r 2 , r being the distance between the field and source points. In order to compute these coefficients a strategy based on Schwartz's distribution theory is employed. In this paper the direct stiffness matrix related to the generic node of the free boundary are computed in closed form.