Local integro-differential equations with domain elements for the numerical solution of partial differential equations with variable coefficients

Sládek, V.; Sládek, J.; Zhang, Ch.

doi:10.1007/s10665-004-3692-y

Cited by 55 publications

(45 citation statements)

References 22 publications

(39 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since the interpolation polynomials are expressed as functions of intrinsic coordinates, the expressions for displacement gradients are not trivial [4] and integrations are to be carried out in the transformed intrinsic space. The local sub-domain Ω c is specified as union of elements adjacent to the interior node y c .…”

Section: Quadrilateral Quadratic Elementsmentioning

confidence: 99%

Stress analysis by local integral equations

Sládek¹,

Sládek²,

Zhang³

2007

WIT Transactions on Modelling and Simulation, Vol 44

Self Cite

View full text Add to dashboard Cite

This paper is a comparative study for various numerical implementations of local integral equations developed for stress analysis in plane elasticity of solids with functionally graded material coefficients. Besides two meshless implementations by the point interpolation method and the moving least squares approximation, the element based approximation is also utilized. The numerical stability, accuracy, convergence of accuracy and cost efficiency (assessed by CPU-times) are investigated in numerous test examples with exact benchmark solutions.

show abstract

Section: Quadrilateral Quadratic Elementsmentioning

confidence: 99%

Stress analysis by local integral equations

Sládek¹,

Sládek²,

Zhang³

2007

WIT Transactions on Modelling and Simulation, Vol 44

Self Cite

View full text Add to dashboard Cite

show abstract

“…Some numerical implementations of the linear LBDIE were presented in [6,7], while slightly different LBDI(D)Es were employed in [8,9].…”

Section: This Reduced the Linear Boundary Value Problem (Bvp) With Vamentioning

confidence: 99%

Direct localized boundary-domain integro-differential formulations for physically nonlinear elasticity of inhomogeneous body

Mikhailov

2005

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

Abstract. A static mixed boundary value problem of physically nonlinear elasticity for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary linear operator, a non-standard boundary-domain integro-differential formulation of the problem is presented, with respect to the displacements and their gradients. Using a cut-off function approach, the corresponding localized parametrix is constructed to reduce the nonlinear boundary value problem to a nonlinear localized boundary-domain integro-differential equation.Algorithms of mesh-based and mesh-less discretizations are presented resulting in sparsely populated systems of nonlinear algebraic equations.

show abstract

“…Another possibility is the Other alternatives worth mentioning adopt weak or non-singular test functions, e.g. [16,17]. Such alternatives may also be applied to the present title problem.…”

Section: Introductionmentioning

confidence: 99%

The boundary element‐free method for elastoplastic implicit analysis

Miers

Telles

2008

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYA meshless procedure, based on boundary integral equations, is proposed to analyze elastoplastic problems. To cope with non-linear problems, the usual boundary element method introduces domain discretization cells, often considered a 'drawback' of the method. Here, to get rid of the standard element and cell, i.e. boundary and domain discretization, the orthogonal moving least squares (also known as improved moving least squares) method is used. The algorithm adopted to solve these particular inelastic nonlinear problems is a well-established, criterion-independent implicit procedure, previously developed by the authors. Comparative results are presented at the end to illustrate the effectiveness of the proposed techniques.

show abstract

Local integro-differential equations with domain elements for the numerical solution of partial differential equations with variable coefficients

Cited by 55 publications

References 22 publications

Stress analysis by local integral equations

Stress analysis by local integral equations

Direct localized boundary-domain integro-differential formulations for physically nonlinear elasticity of inhomogeneous body

The boundary element‐free method for elastoplastic implicit analysis

Contact Info

Product

Resources

About