Boundary element method analysis of stationary thermoelasticity problems in non-homogeneous media

This paper presents an advanced BEM formulation for the solution of stationary problems of thermoelasticity taking into consideration the thermally induced non-homogeneity. An iterative scheme is used to determine the displacement fields because the formulation contains a domain-type integral with displacements. As compared with the existing BEM formulation, this one does not contain a domain integral of the temperature field and, furthermore, the integral representation of stresses is written in the regularized from. Consequently, all the integrals can be computed numerically by using the regular Gaussian quadrature.     

Application of boundary element method to 3-D problems of coupled thermoelasticity

This paper deals with a new boundary element method for analysis of the quasistatic problems in coupled thermoelasticity. Through some mathematical manipulation of the Navier equation in elasticity, the heat conduction equation is transformed into a simpler form, similar to the uncoupled-type equation with the modified thermal conductivity which shows the coupling effects. This procedure enables us to treat the coupled thermoelastic problems as an uncoupled one, A few examples are computed by the proposed BEM, and the results obtained are compared with the analytical ones available in the literature, whereby the accuracy and versatility of the proposed method are demonstrated.     

Boundary element analysis in thermoelasticity with and without internal cells

In this paper, a set of internal stress integral equations is derived for solving thermoelastic problems. A jump term and a strongly singular domain integral associated with the temperature of the material are produced in these equations. The strongly singular domain integral is then regularized using a semi‐analytical technique. To avoid the requirement of discretizing the domain into internal cells, domain integrals included in both displacement and internal stress integral equations are transformed into equivalent boundary integrals using the radial integration method (RIM). Two numerical examples for 2D and 3D, respectively, are presented to verify the derived formulations. Copyright © 2003 John Wiley & Sons, Ltd.     

Boundary element analysis of thermoelastic contact problems

A boundary element method (BEM) is applied to thermoelastic contact problems where thermal resistance at the contact interface is not negligible. The displacement, traction, temperature and temperature gradient in the contact zone are unknown quantities to be determined numerically. Due to the existence of thermal resistance, temperature and stress fields are mutually coupled. To solve the problem, two kinds of methods are presented. In the first method, the solution is obtained by minimizing a suitably defined objective function. In the second method, discretized equations of each of the bodies in contact are computed alternately until all prescribed boundary conditions are satisfied. The applicability of these methods to practical problems is examined through several numerical examples.     

Boundary element analysis of stress intensity factor KI in some two-dimensional dynamic thermoelastic problems

This paper presents a numerical technique for the calculation of stress intensity factor as a function of time for coupled thermoelastic problems. In this task, effect of inertia term considering coupled theory of thermoelasticity is investigated and its importance is shown.A boundary element method using Laplace transform in time-domain is developed for the analysis of fracture mechanic considering dynamic coupled thermoelasticity problems in two-dimensional finite domain. The Laplace transform method is applied to the time-domain and the resulting equations in the transformed field are discretized using boundary element method. Actual physical quantities in time-domain is obtained, using the numerical inversion of the Laplace transform method.The singular behavior of the temperature and stress fields in the vicinity of the crack tip is modeled by quarter-point elements. Thermal dynamic stress intensity factor for mode I is evaluated using J-integral method. By using J-integral method effects of inertia term and other terms such as strain energy on stress intensity factor may be investigated separately and their importance may be shown. The accuracy of the method is investigated through comparison of the results with the available data in literature.     

Boundary element analysis of two-dimensional elastoplastic contact problems

A general boundary element formulation for contact problems, capable of dealing with local elastoplastic effects and friction, is presented. Both conforming and non-conforming problems may be analysed. The contact problem is solved by means of a direct constraint technique, in which compatibility and equilibrium conditions are directly enforced in the general system of equations. The contact areas are modelled with linear interpolation functions, and quadratic interpolation functions are used everywhere else. Elastoplasticity is solved by a BEM initial strain approach The Von Mises yield criterion with its associated flow rule is adopted. Both perfectly plastic and work hardening materials are studied in the proposed formulation.

An incremental loading technique is proposed, which allows accurate development of the loading history of the problem. The non-linear nature of these problems demands the use of an iterative procedure, to determine the correct frictional conditions at every node of the contact area and the value of the plastic strains at selected points where local yielding may have occurred. Several numerical examples are presented to demonstrate the efficiency of the proposed formulation.     

Boundary element analysis of two-dimensional elastoplastic contact problems

In this paper a boundary element method for two-dimensional elastoplastic stress analysis of frictional contact problems is presented. The bodies in contact are treated as separate regions. The contact conditions are used to join the different system of equations for different regions of contacted bodies and, hence, an overall system of equation is obtained. An incremental and iterative procedure can be used to find the contact load, or the contact extent and the proper contact conditions. To include the plastic deformation in the analysis, the initial strain algorithm is employed. Elastic-perfectly plastic or work-hardening material behaviour can be assumed. For the numerical analysis, an isoparametric three-noded line elements are used to represent the boundary and eight-noded quadrilateral or six-noded triangular elements are used for the interior of the domain. The displacement rates and traction rates are assumed to vary quadratically and the shape functions for the interior strain rates are also of quadratic type. As an example, the behaviour of an elastic and elastoplastic body with a smooth, circular inclusion under the increasing load is presented.     

Boundary element analysis of nonlinear water wave problems

A new boundary element technique based on Green's formula is applied to the analysis of nonlinear water wave problems. The problems are formulated mathematically as two-dimensional nonlinear initial-boundary value problems in terms of a velocity potential, assuming the fluid to be inviscid and incompressible, and the flow to be irrotational. In the present paper, two kinds of wave-making problems are analysed: (1) a tsunami generated by sea bed elevation; (2) generation, propagation and run-up on a vertical wall of a solitary wave. Numerical results obtained by the present method are compared with available experimental data and analytical solutions. Excellent agreements are obtained.     

Boundary element analysis of 3-D magnetostatic problems usingscalar potentials

A boundary element formulation for 3-D nonlinear magnetostatic field problems using the total scalar potential and its normal derivative as unknowns is described. The boundary integral equation is derived from a differential equation for the total scalar potential where a nonlinear operator term can be separated from a linear term. The nonlinear term leads to a volume integral which can be treated as a known forcing function within an iterative solution process. An additional forcing term results from the magnetic excitation coil system. It is shown that the line integral of the magnetic source field which can be defined outside of the current-carrying regions as a gradient of a scalar potential acts as an excitation term. The proposed method is applied to a test problem where an iron cube immersed in the magnetic field of a cylindrical coil is investigated. The numerical results for different saturation stages are compared with finite element method (FEM) calculations. The comparison with FEM calculations shows a good agreement only in highly saturated iron parts     

Finite element,boundary element and coupled analysis of unbounded problems in elastostatics

The implementation of a combined boundary element-finite element analysis capability is discussed. A comparison is then made between the finite element, boundary element and coupled method as applied to unbounded problems in elasticity and plasticity.     

Boundary element formulation for the coupled stretching-bending analysis of thin laminated plates

The boundary integral equations for the coupled stretching-bending analysis of thin laminated plates involve an integral which will be singular when the field point approaches the source point. To avoid the singular problem occurring in the numerical programming, the boundary integral equations are modified in which the integrals of singular part are integrated analytically. The analytical solutions for the free term coefficients and singular integrals are obtained in explicit closed-form. By dividing the boundary into elements and using suitable interpolation polynomials for basic functions, the set of equations necessary for boundary element programming are written explicitly for regular nodes and corner nodes. The equations for the determination of displacements and stresses at internal points are also presented in this paper.     

Boundary element frequency domain formulation for dynamic analysis of Mindlin plates

A new boundary element formulation for analysis of shear deformable plates subjected to dynamic loading is presented. Fundamental solutions for the Mindlin plate theory are derived in the Laplace transform domain. The characteristics of the three flextural waves are studied in the time domain. It is shown that the new fundamental solutions exhibit the same strong singularity as in the static case. Two numerical examples are presented to demonstrate the accuracy of the boundary element method and comparisons are made with the finite element method. Copyright © 2006 John Wiley & Sons, Ltd.     

Boundary element analysis of an integral equation for three-dmensional crack problems

In another paper, the authors proposed an integral equation for arbitrary shaped three-dimensional cracks. In the present paper, a discretization of this equation using a tensor formalism is formulated. This approach has the advantage of providing the displacement discontinuity vector in the local basis which varies as a function of the point of the crack surface. This also facilitates the computation of the stress intensity factors along the crack edge. Numerical examples reported for a circular crack and a semi-elliptical surface crack in a cylindrical bar show that one can obtain good results, using few Gaussian points and no singular elements.     

Boundary element method for thermoelastoplastic problems

In this paper, we present the boundary integral formulation for inelastic stationary thermoelasticity including thermally induced non-homogeneity. Generally, the unique BEM formulation for crack problems is achieved by using the traction boundary integral equations which are now considered in a non-singular form. Both the two- and three-dimensional boundary value problems are analysed simultaneously. Numerical examples for 2-D problems are presented, in order to illustrate the suitability of this boundary element approach in the inelastic thermoelasticity.     

Boundary integral equations and the boundary element method for fracture mechanics analysis in 2D anisotropic thermoelasticity

This paper develops the Somigliana type boundary integral equations for fracture of anisotropic thermoelastic solids using the Stroh formalism and the theory of analytic functions. In the absence of body forces and internal heat sources, obtained integral equations contain only curvilinear integrals over the solid’s boundary and crack faces. Thus, the volume integration is eliminated and also there is no need to evaluate integrals over the contours in the mapped temperature domain as it was done before. In addition to finite solids, the case of an infinite anisotropic medium with a remote thermal load is also studied. The dual boundary element method for fracture of anisotropic thermoelastic solids is developed based on the obtained boundary integral equations. Presented numerical examples show the validity and efficiency of the obtained equations in the analysis of both finite and infinite solids with cracks.     

A fast multipole boundary element method for solving two-dimensional thermoelasticity problems

A fast multipole boundary element method (BEM) for solving general uncoupled steady-state thermoelasticity problems in two dimensions is presented in this paper. The fast multipole BEM is developed to handle the thermal term in the thermoelasticity boundary integral equation involving temperature and heat flux distributions on the boundary of the problem domain. Fast multipole expansions, local expansions and related translations for the thermal term are derived using complex variables. Several numerical examples are presented to show the accuracy and effectiveness of the developed fast multipole BEM in calculating the displacement and stress fields for 2-D elastic bodies under various thermal loads, including thin structure domains that are difficult to mesh using the finite element method (FEM). The BEM results using constant elements are found to be accurate compared with the analytical solutions, and the accuracy of the BEM results is found to be comparable to that of the FEM with linear elements. In addition, the BEM offers the ease of use in generating the mesh for a thin structure domain or a domain with complicated geometry, such as a perforated plate with randomly distributed holes for which the FEM fails to provide an adequate mesh. These results clearly demonstrate the potential of the developed fast multipole BEM for solving 2-D thermoelasticity problems.     

An effective finite element modeling/analysis approach for dynamic thermoelasticity due to second sound effects

Of interest here are dynamic thermoelastic problems influenced by second sound effects. In this regard, the effect of the so called heat waves on solid continua is investigated employing a unified explicit computational architecture which uses the finite element method. The approach is robust and effective for transient interdisciplinary thermal-structural modeling/analysis. The non-classical relaxation model of Green and Lindsay (1972) involving two relaxation times is employed in the present work. Numerical simulations relevant to thermal shock problems in an elastic half-space are described for stainless steel via two different illustrative test cases.     

Boundary element analysis of three-dimensional crack problems in two joined transversely isotropic solids

The present paper presents a boundary element analysis of penny-shaped crack problems in two joined transversely isotropic solids. The boundary element analysis is carried out by incorporating the fundamental singular solution for a concentrated point load in a transversely isotropic bi-material solid of infinite space into the conventional displacement boundary integral equations. The conventional multi-region method is used to analyze the crack problems. The traction-singular elements are employed to capture the singularity around the crack front. The values of the stress intensity factors are obtained by using crack opening displacements. The numerical scheme results are verified with the closed-form solutions available in the literature for a penny-shaped crack parallel to the plane of the isotropy of a homogeneous and transversely isotropic solid of infinite extent. The new problem of a penny-shaped crack perpendicular to the interface of a transversely isotropic bi-material solid is then examined in detail. The crack surfaces are subject to the three normal tractions and the uniform shear traction. The associated stress intensity factor values are obtained and analyzed. The present results can be used for the prediction of the stability of composite structures and the hydraulic fracturing in deep rock strata and reservoir engineering.     

Boundary element implementation of doubly periodic inclusion problems

A rectangular cell with the given boundary condition is cut from doubly period inclusion problems. Based on the single-domain and the sub-domain boundary element methods, numerical solution of the rectangular cell can be obtained. Following this, effective elastic properties for various doubly periodic inclusion problems can be calculated. Numerical results show the rightness and effectiveness of the present method.     

One-dimensional inverse thermoelasticity problems

The unique solvability of two one-dimensional inverse problems on determining the coefficients of thermoelasticity equations is established; the solution algorithm for these problems is indicated and numerical calculations are given.State Pedagogical Institute, Gynadzha. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 1, pp. 98–104, July, 1993.