A new boundary element formulation is introduced for the treatment of gravitational and centrifugal body forces in axisymmetric elastic media. This new formulation is based on the method of particular integrals, which require neither volume nor surface integration for the treatment of body forces. Particular integrals for both gravitational and centrifugal body forces are derived and all kernel functions are defined in an appendix. The formulation is implemented into a multiregion system that utilizes quadratic isoparametric shape functions to model the geometry and field variables on the boundary of the body. A number of examples of practical interest have been included to demonstrate the power and versatility of the present formulation.

New Axisymmetric BEM Formulation for Body Forces Using Particular Integrals

A boundary integral equation method for axisymmetric elastic contact problems

A boundary element method for axisymmetric soil consolidation

A boundary element method is developed for problems of quasistatic axisymmetric thermoelasticity. Unlike previous approaches, this new time domain formulation is written exclusively in terms of surface quantities, thereby eliminating the need for volume discretization. Furthermore, since the exact three-dimensional infinite space fundamental solutions are employed, very accurate solutions are obtainable, including the determination of surface stresses.

In the integral formulation, the fundamental solutions are separated into steady-state and transient components. The steady-state portion, which contains all of the singularities, is integrated analytically in the circumferential direction, yielding the familiar axisymmetric kernels. The remaining non-singular transient integrands are treated by a combination of analytical and numerical quadrature.

The method is implemented in a general purpose boundary element code, which includes multiregion capability along with higher order conforming surface elements. Several numerical examples are provided to illustrate the validity of the formulation and the attractiveness of this approach for practical engineenring analysis.

Time dependent axisymmetric thermoelastic boundary element analysis

Axisymmetric problems for an elastic halfspace are commonly analyzed by the boundary element (BE) method by employing the axisymmetric fundamental solution for the fullspace. In such cases, the discretization of the free surface is required, with its truncation at an appropriate location from the axis of symmetry. This paper presents the BE implementation of the axisymmetric fundamental solution for an elastic halfspace, given in terms of integrals of the Lipschitz–Hankel type, that satisfies in advance the boundary condition of zero traction on the free surface and the decay of displacements in the far field. Explicit equations for post-processing the results at internal points are provided, as well as adequate numerical schemes to evaluate the boundary integrals arising in the method. This formulation can be easily implemented in existing BE computational codes for axisymmetric fullspace problems, requiring only a few modifications. Numerical results are provided to validate the proposed formulation.

Boundary element formulation of axisymmetric problems for an elastic halfspace

The boundary integral equation (BIE) numerical method for linear elastic stress analysis is applied to axisymmetric problems which also involve temperature variations due to steady-state thermal conduction. The boundary of the two-dimensional solution domain is discretized into isoparametric quadratic line elements, which provide an excellent modelling capability. Satisfactory agreement is obtained with both exact analytical solutions for test problems and numerical results obtained by the finite difference and finite element methods. The BIE method is applied to the problem of a hollow cylinder with an external semi-circular groove, subjected to axial tensile loading and a temperature difference across the cylinder wall. The results emphasise the very high stress concentrations which can be obtained when the effects of thermal and mechanical loading are superimposed. An important practical advantage of the BIE method is the small amount of labour involved in preparing the mesh data.

Boundary integral equation analysis of axisymmetric thermoelastic problems

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Boundary integral equation analysis of axisymmetric thermoelastic problems