P. K. Banerjee

Boundary element analysis of cracks in thermally stressed planar structures

Abstract The evaluation of stress intensity factors is important for the assessment of structural integrity of flawed structures. The boundary element method is used in the present work for the computation of steady-state and time-dependent stress intensity factors of cracks in thermally loaded structures. While many boundary and volume integral based formulations are available for the treatment of thermoelastic problems in solids, the present analysis is based on a recently developed boundary-only formulation. Crack-tip elements that accurately model the behavior of displacement, temperature fields and singularity of traction, flux fields are used for the accurate evaluation of stress intensity factors.

Two-dimensional transient wave-propagation problems by time-domain BEM

Abstract In this paper, an advanced formulation of time-domain Boundary Element Method (BEM) for linear elastodynamics is used to study a number of problems involving wave propagation through half-space as well as multi-layered soils. The algorithm incorporates isoparametric quadratic elements which facilitate proper modelling of problem geometry and can represent the field variables in dynamic problems very accurately, which are very often wavy in nature. Also higher order temporal variation of functions is introduced. Improved techniques are employed for the accurate evaluation of both the singular and non-singular spatial integrals. Most importantly, this formulation incorporates simpler and better behaved kernels compared to those that have appeared in the recent BEM literature by the present and other previous researchers. With all these new and efficient features the present formulation is superior to the existing ones and as such represents a very effective tool for solving 2D transient wave propagation problems, especially in infinite and semi-infinite domains where other numerical methods have considerable difficulty in producing accurate solutions.

Development of a boundary element method for time-dependent planar thermoelasticity

Abstract A new boundary element method is developed for two-dimensional quasistatic thermoelasticity. This time domain formulation involves only surface quantities. Consequently, volume discretization is completely eliminated and the method becomes a viable alternative to the usual finite element approaches. After presenting a brief overview of the governing equations, boundary integral equations for coupled quasistatic thermoelasticity are derived by starting with existing fundamental solutions along with an appropriate reciprocal theorem. Details of a general purpose numerical implementation are then discussed. Next. boundary element methods for the two more practical theories, uncoupled quasistatic and steady-state thermoelasticity, are developed directly from limiting forms of the coupled formulation. Several numerical examples are provided to illustrate the validity and attractiveness of the boundary element approach for this entire class of problems.

Fundamental solutions of biot's equations of dynamic poroelasticity

Abstract Fundamental solutions pertaining to Biots equation of three-dimensional dynamic poroelasticity are derived in the Laplace transform domain. These solutions define the displacement field in fluid-saturated media due to point forces in the solid and fluid phases. In addition, for the two extreme cases of a medium with low and high permeabilities, time domain approximations of the fundamental solutions are derived by inverting Laplace transform expressions. Finally, numerical results are presented to highlight the salient features of the problem as well as investigate the accuracy of the time domain solutions. These analytical expressions are also used to define the equivalent one-phase material properties for the more usual undrained dynamic analyses.

Elastic Analysis of Three-Dimensional Solids with Fiber Inclusions by Bem

A very efficient method of analysis for the elastic behavior of three-dimensional solids with a large number of embedded fiber inclusions has been developed. For specific applications to the analysis of cylindrical shaped fiber inclusions significant gain in efficiency can be achieved by defining these inclusions by a system of curvilinear line elements with a prescribed diameter and by assuming a variation in the traction and displacement field in the circumferential directions in terms of a trigonometric shape function together with a linear or quadratic variation along the longitudinal direction. The resulting integrals are then treated semi-analytically. A number of examples of the analysis which has been developed for composite elements are described.

Boundary element methods in three-dimensional thermoelasticity

Abstract A boundary element method is developed for the solution of time-dependent problems in three-dimensional thermoelasticity. The time domain, boundary-only formulation represents the first of its kind for quasistatic analysis, which by definition considers transient heat conduction, but ignores the effects of inertia. By eliminating the need for volume discretization, the method becomes an attractive alternative to finite element analysis for this class of problems. Additionally, because an exact Greens function is used in the interior, steep thermal gradients can be captured much more readily than with standard domain-based methods. The presentation includes details of the fundamental solution, a derivation of the boundary integral equations, and an overview of a general purpose numerical implementation. This implementation permits the solution of large, multiregion problems with arbitrary geometry and boundary conditions. Several examples are included to validate the proposed method, as well as to highlight its usefulness.

Two- and three-dimensional transient thermoelastic analysis by BEM via particular integrals

Abstract Particular integral formulations are presented for two- and three-dimensional transient uncoupled thermoelastic analysis. These formulations differ from previous particular integral formulations in that the equation of uncoupled thermoelasticity including the heat conduction equation is fully satisfied to obtain particular integrals. The equation of the steady-state thermoelasticity is now used as the complementary solution and two global shape functions are considered to approximate the transient term of the heat conduction equation so that two sets of particular integrals could be derived. The numerical results for both sets of particular integrals are given for three example problems and compared with their analytical solutions.

Advanced development of boundary element method for two-dimensional dynamic elasto-plasticity

Abstract In this paper, the formulation and numerical implementation of two-dimensional transient dynamic elasto-plasticity by the boundary element method is presented. This formulation considers material non-linearity and is based on an initial stress approach. It is the first ever attempt to solve two-dimensional dynamic plasticity problems by the boundary element method. The boundary integral equations are cast in an incremental form and are solved using a time stepping technique. The Newton-Raphson iterative scheme is adopted in conjunction with the non-linear constitutive equation to determine the incremental initial stresses. This formulation incorporates quadratic isoparametric elements for both the boundary and volume discretizations. The accuracy and stability of the methodology are demonstrated via numerical examples. It has been implemented in a general purpose, multi-region boundary element software known as GPBEST.

A boundary element method for axisymmetric soil consolidation

Abstract The development of a time domain boundary element method for axisymmetric quasistatic poroelasticity is discussed. This new formulation, for the complete Biot consolidation theory, has the distinct advantage of being written exclusively in terms of boundary variables. Thus, no volume discretization is required, and the approach is ideally suited for geotechnicul problems involving media of infinite extent. In the presentation, the required axisymmetric integral equations and kernel functions are first developed from the corresponding three-dimensional theory. In particular, emphasis is placed on the analytical and numerical treatment of the kernels. This is followed by an overview of the numerical implementation, and a demonstration of its merits via the consideration of several examples.

Advanced inelastic analysis of solids by the boundary element method

Abstract Two boundary element solution algorithms are used for solving a range of elastoplastic and thermoplastic problems. The first algorithm is the conventional iterative procedure in which the unknown boundary solution and the initial stress (or strain) rates are found together in an incremental iterative fashion. The second algorithm is a new variable stiffness type approach in which the incremental boundary solution is obtained in a direct (non-iterative) manner. This new approach is presented in a general manner for axisymmetric, two- and three-dimensional analyses. The formulation is implemented in a general purpose, multi-region system that utilizes quadratic isoparametric shape functions to model the geometry and field variables of the body and can admit up to 15 substructured regions of different material properties.