A cell-less BEM formulation for axisymmetric elastoplasticity via particular integrals

This study deals with the particular integral formulation for purely axisymmetric elastoplastic analysis. The axisymmetric elastostatic equation is used for the complementary solution. The axisymmetric particular integrals for displacement and strain rates are derived by integrating three-dimensional formulation along the circumferential direction leading to elliptic integrals. The particular integrals for stress and traction rates are obtained by using the stress–strain and traction–stress relations. The Newton–Raphson algorithm for the plastic multiplier is used to solve the system equation. The numerical results for four example problems are given and compared with their analytical solutions or those by other BEM and FEM programs to demonstrate the accuracy of the present formulation. Generally, agreement among all of those results is satisfactory.     

A new BEM formulation for tow- and three-dimensional elastoplasticity using particular integras

New two- and three-dimensional boundary element formulations are developed for elastoplastic stress analysis. These new procedures differ from previous work in that volume integration is not required to incorporate the non-linear effects in the analysis. Instead, initial stess rates are introduced in the boundary element system via particular integrals. The present formulation is implemented in a general purpose, multi-region system, and examples are presented to demonstrate the accuracy and versatility of the method.     

A BEM formulation for inelastic transient dynamic analysis using domain decomposition and particular integrals

This study deals with the domain decomposition method and particular integrals for multi-region inelastic transient dynamic analysis. The particular integral formulation for single-region inelastic transient dynamic analysis is obtained by eliminating the acceleration volume integral and treating the initial stress term by volume cell. The Houbolt time integration scheme is used for the time- marching process. The Newton-Raphson algorithm for plastic multiplier is used to solve the system equation. In order to extend to multi-region problems, the domain decomposition method is examined. The domain of the original problem is subdivided into subregions. The interface boundary conditions are updated by using the iterative coupling employing Schwarz algorithm. Numerical results of two example problems are given to demonstrate the validity and accuracy of the present formulation.     

Some remarks on definitions and, in particular, on the definition of the term calibration

Confucius (Analects xiii:3) ‘It is not possible to haveany valid argument until rigorously defined terms are agreed’. In radiation protection dosimetry, we perhaps need to take asthe fundamental sources of our definitions for personal dosimetryand area monitoring, mainly those three committees—theJoint Committee for Guides in Metrology (JCGM), which givesdefinitions for metrology generally; the International Commissionon Radiation Units and Measurements (ICRU), which gives basicphysical quantities and units for ionising radiation; and theInternational Commission on Radiological Protection (ICRP) forquantities considering the health effect of ionising radiation,for example effective dose, equivalent dose and the qualityfactor/linear energy transfer function. The JCGM, chaired by the Director of the BIPM, is formed bythe seven international organisations that had prepared theoriginal versions of the     

BEM formulation for reinforced plates

This article presents a BEM formulation developed to analyse reinforced plate bending. The reinforcements are formulated using a simplified scheme based on applying an initial moment field adopted to locally correct the stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. The increase in system stiffness due to the reinforcements can be taken into account independently for each coefficient. Thus, one can conveniently reduce the number of degrees of freedom required in considering the reinforcement. Only one degree-of-freedom is required at each internal node when taking into account only the flexural stiffness of beams. Examples are presented to confirm the accuracy of the formulation.     

Stochastic second-order BEM perturbation formulation

This paper presents the stochastic second order moment perturbation approach to the classical deterministic Boundary Element Method (BEM) formulation. Numerous applications of such a formulation in different problems of stochastic mechanics, especially in the field of computational modeling of structural defects in homogeneous and composite materials occurring randomly in solids and engineering structures, were the main reasons to introduce the proposed model. The stochastic boundary element method (SBEM) formulation of the general linear elasticity boundary value has been provided together with an appropriate discretization. The equations describing the expected values and the covariances of stress and strain tensors for points lying on the boundary and inside the region are considered. This set of equations constitutes a formal mathematical statement of the problem and is suitable for computational implementation.     

Displacement gradients in BEM formulation for small strain plasticity

In the present work, we propose a consistent derivation of the regularized integral representations for displacement gradients within the boundary element formulation for solution of small strain plasticity problems. The regularization is carried out for both the domain and boundary integrals before any discretization and approximation of integral densities. Two kinds of the integral representations are derived with the leading singularity of the integral kernels being either hypersingularity or strong singularity. Both the two- and three-dimensional problems are considered simultaneously.     

Some fundamental solutions for the Kirchhoff,Reissner and Mindlin plates and a unified BEM formulation

We derive analytical solutions for the deflection of thin circular plates, which are loaded by centrally located concentrated bending moments and transverse forces. Green's functions for clamped and simply supported plates are presented. Reduction of these Green's functions leads to the corresponding fundamental solution for the Kirchhoff plate bending model (K problem). This fundamental solution reduces to those obtained through the direct simplification of the fundamental solution for the sixth-order Reissner and Mindlin plate bending models (RM problem). This allows to decompose each fundamental tensor of the problem RM into the sum of the fundamental tensor of the problem K and a correction tensor (Sh problem), which contains the contribution of the shear strains, e.g. U_ij^RM(r)=U_ij^K(r)+U_ij^Sh(r). Within the boundary element analysis this enables the investigation of the contributions of the shear strains to the solutions of Reissner and Mindlin plate bending models, as corrections of the Kirchhoff values, all determined from the same BEM code. This opens up new possibilities for the analysis of plates by the BEM.     

Elastodynamics by BEM: a new direct formulation

A new direct BE formulation is proposed for the solution of elastodynamic problems. An analytical regularization procedure is devised via an integration‐by‐parts technique without introducing any hypothesis about either the discretization of the boundary geometry or the space–time interpolation of the elastic fields involved. The only requirement is for continuity in the displacement field. The regularization of the integral equations for static elasticity using the same approach, already available in the literature, is presented as a particular case of the general procedure introduced herein. The numerical implementation of this technique is discussed and two‐dimensional examples are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

An implicit BEM formulation to model strong discontinuities in solids

A boundary element method (BEM) formulation to predict the behavior of solids exhibiting displacement (strong) discontinuity is presented. In this formulation, the effects of the displacement jump of a discontinuity interface embedded in an internal cell are reproduced by an equivalent strain field over the cell. To compute the stresses, this equivalent strain field is assumed as the inelastic part of the total strain. As a consequence, the non-linear BEM integral equations that result from the proposed approach are similar to those of the implicit BEM based on initial strains. Since discontinuity interfaces can be introduced inside the cell independently on the cell boundaries, the proposed BEM formulation, combined with a tracking scheme to trace the discontinuity path during the analysis, allows for arbitrary discontinuity propagation using a fixed mesh. A simple technique to track the crack path is outlined. This technique is based on the construction of a polygonal line formed by segments inside the cells, in which the assumed failure criterion is reached. Two experimental concrete fracture tests were analyzed to assess the performance of the proposed formulation.     

Some remarks on strong fibonacci pseudoprimes

Necessary and sufficient conditions are given for an odd composite integern to be a Fibonacci pseudoprime of them ^th kind for allm. One consequence of this characterization is that any such pseudoprime has to be a Carmichael number.This author expresses his special thanks to the School of Information Engineering at Teesside Polytechnic, Middlesbrough, England, for its support and hospitality during a visiting appoint of 3 months in 1989, when this paper was written     

Transient dynamic elastoplastic analysis by the time-domain BEM formulation

This paper presents a time-domain BEM formulation applied to the solution of transient dynamic elastoplastic problems. The initial stress approach is adopted to solve the elastoplastic problem. Linear time variation is assumed for the displacements and initial stress components whereas traction components are assumed to have a constant time variation. Boundary discretization employs linear elements and the part of the domain where plastic deformation is expected to occur is discretized by employing linear triangular cells. Time integrals are computed analytically, boundary integrals are computed numerically and the domain integrals are computed by following a semi-analytical procedure. A numerical example is presented and the results are compared with another BEM formulation.     

A new BEM formulation for the acoustic eigenfrequency analysis

A new boundary element formulation has been developed for two- and three-dimensional acoustic eigenfrequency analyses. The formulation is based on the well known method of constructing a solution of a differential equation in terms of a complementary function and particular integral. An advanced isoparametric implementation with automatic error control in the integration is used. A number of realistic examples of application to automotive acoustic cavities are described.     

CQM-based BEM formulation for uncoupled transient quasistatic thermoelasticity analysis

A boundary element method based on the convolution quadrature method for the numerical solution of uncoupled transient thermoelasticity problems is presented. In the proposed formulation, the time-domain integral equation is numerically approximated by a quadrature formula whose weight factors are computed by means of integral expressions involving the Laplace transform of the fundamental solution. Compared with other numerical methods that operate directly in the Laplace transformed domain, the proposed formulation requires only the definition of the time-step used by the procedure of integration, and does not need special techniques of inversion from the Laplace-domain to the time-domain. Numerical examples of transient thermoelasticity problems are presented to show the versatility and accuracy of the method.     

Initial conditions contribution in a BEM formulation based on the convolution quadrature method

This work presents a two‐dimensional boundary element method (BEM) formulation for the analysis of scalar wave propagation problems. The formulation is based on the so‐called convolution quadrature method (CQM) by means of which the convolution integral, presented in time‐domain BEM formulations, is numerically substituted by a quadrature formula, whose weights are computed using the Laplace transform of the fundamental solution and a linear multistep method. This BEM formulation was initially developed for scalar wave propagation problems with null initial conditions. In order to overcome this limitation, this work presents a general procedure that enables one to take into account non‐homogeneous initial conditions, after replacing the initial conditions by equivalent pseudo‐forces. The numerical results included in this work show the accuracy of the proposed BEM formulation and its applicability to such kind of analysis. Copyright © 2006 John Wiley & Sons, Ltd.     

Computation of time and space derivatives in a CQM-based BEM formulation

This work proposes an approach for the numerical computation of time and space derivatives of the time-domain solution of scalar wave propagation problems by means of a boundary element method formulation. Here, this formulation employs the so-called convolution quadrature method. Non-homogeneous initial conditions are taken into account by means of a general procedure, known as initial condition pseudo-force procedure, which replaces the initial conditions by equivalent pseudo-forces. The boundary integral equation with initial conditions contribution is differentiated analytically and the quadrature weights of the standard formulation are transformed in order to compute time and space derivatives at interior points. Numerical examples are presented to show the efficiency of the implemented formulation.     

BEM solution of stochastic seawater intrusion problems

In this paper, the stochastic saltwater–freshwater interface location in coastal aquifer is sought, subject to the uncertainty of input parameters such as hydraulic conductivity, freshwater outflow, and pumping rate. The boundary element method, combined with an optimization technique, is used as the tool for deterministic solution to search for the interface location. A second order perturbation technique is employed to find the statistical moments of the prediction. Three saltwater intrusion examples of different geometries are examined.