Lower bound limit analysis by bem: Convex optimization problem and incremental approach

The lower bound limit approach of the classical plasticity theory is rephrased using the Multidomain Symmetric Galerkin Boundary Element Method, under conditions of plane and initial strains, ideal plasticity and associated flow rule. The new formulation couples a multidomain procedure with nonlinear programming techniques and defines the self-equilibrium stress field by an equation involving all the substructures (bem-elements) of the discretized system. The analysis is performed in a canonical form as a convex optimization problem with quadratic constraints, in terms of discrete variables, and implemented using the Karnak.sGbem code coupled with the optimization toolbox by MatLab. The numerical tests, compared with the iterative elastoplastic analysis via the Multidomain Symmetric Galerkin Boundary Element Method, developed by some of the present authors, and with the available literature, prove the computational advantages of the proposed algorithm.     

Harmonic analysis of shear deformable orthotropic cracked plates using the Boundary Element Method

In this work, the modal and harmonic analysis of orthotropic shear deformable cracked plates using a direct time-domain Boundary Element Method formulation based on the elastostatic fundamental solution of the problem is presented. The Radial Integration Method was used for the treatment of domain integrals involving distributed domain applied loads and those related with inertial mass forces. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed formulation.     

The boundary element analysis of cracked stiffened sheets,reinforced by adhesively bonded patches

This paper presents a formulation based on the Dual Boundary Element Method and on the Dual Reciprocity Method for the analysis of thin cracked metal sheets to which thin metal patches and stiffeners are adhesively bonded. The stiffened cracked sheet is modelled with the Dual Boundary Element Method. Adhesive shear stresses are modelled as action–reaction body forces exchanged by the sheet and patches. The Dual Reciprocity Method is used to avoid the discretization of the patches attachment domain into internal cells. Several examples are presented to demonstrate the efficiency and robustness of the method developed. The examples include sheets with embedded or edge cracks, stiffened or not, to which single or double patches are adhesively bonded. © 1998 John Wiley & Sons, Ltd.     

Dynamic analysis of Timoshenko beams by the boundary element method

A Boundary Element Method formulation is developed for the dynamic analysis of Timoshenko beams. Based on the use of not time dependent fundamental solutions a formulation of the type called as Domain Boundary Element Method arises. Beside the typical domain integrals containing the second order time derivatives of the transverse displacement and of the rotation of the cross-section due to bending, additional domain integrals appear: one due to the loading and the other two due to the coupled differential equations that govern the problem. The time-marching employs the Houbolt method. The four usual kinds of beams that are pinned–pinned, fixed–fixed, fixed–pinned and fixed–free, under uniformly distributed, concentrated, harmonic concentrated and impulsive loading, are analyzed. The results are compared with the available analytical solutions and with those furnished by the Finite Difference Method.     

A simple Kelvin and Boltzmann viscoelastic analysis of three-dimensional solids by the boundary element method

This paper presents a three-dimensional Boundary Element formulation for the analysis of simplified viscoelastic bodies without using internal cells. Two different constitutive models are considered. The first and simplest one is the Kelvin model, which does not consider instantaneous responses. The second, Boltzmann model, considers both instantaneous and viscous behaviour of materials. An appropriate kinematical relation together with differential viscoelastic constitutive representations are employed in order to built the proposed Scheme. Spatial approximations are applied for boundary elements before time solution. The proposed technique results in a time marching process that does not use relaxation (or creep) functions to recover viscous behaviour. Some examples are shown in order to demonstrate the accuracy and stability of the technique when compared to analytical solutions.     

Alternative time-marching schemes for elastodynamic analysis with the domain boundary element method formulation

This work presents alternative time-marching schemes for performing elastodynamic analysis by the Boundary Element Method. The use of the static fundamental solution and the maintenance of the domain integral associated to the accelerations characterize the formulation employed in this work. It is called D-BEM, D meaning domain. Time response is obtained by employing step-by-step time-marching procedures similar to those adopted in the Finite Element Method. Among all integration procedures, Houbolt scheme became the most popular used to march in time with D-BEM formulation, in spite of the presence of a high numerical damping. In order to improve the integration, this work presents alternative schemes that can be used to perform elastodynamic analysis by the BEM with a better damping control. In order to verify the accuracy of the proposed scheme, three examples are presented and discussed at the end of this work.     

Testing complete and compact radial basis functions for solution of eigenvalue problems using the boundary element method with direct integration

This paper analyses the performance of the main radial basis functions in the formulation of the Boundary Element Method (DIBEM). This is an alternative for solving problems modeled by non-adjoint differential operators, since it transforms domain integrals in boundary integrals using radial basis functions. The solution of eigenvalue problem was chosen to performance evaluation. Natural frequencies are calculated numerically using several radial functions and their accuracy is evaluated by comparison with the available analytical solutions and with the Finite Element Method as well. The standard radial basis functions have presented similar performance to compact radial functions, being even slightly superior.     

Dynamic behavior of frame structures by boundary integral procedures

The Boundary Element Method is applied to synthesize a set of Boundary Integral Equations representing the uncoupled axial and flexural dynamic behavior of rectilinear Bernoulli–Euler beam elements in the frequency domain. In the sequence, these structural elements are coupled by the sub-region technique to model two-dimensional frame structures, in which the axial and flexural behaviors are coupled. This methodology is used to accurately recover modal data, eigenfrequencies and eigenmodes, of two frame structures. The usual Boundary Element procedure is recast to deliver simultaneously the values of variables at the element boundaries and at an arbitrary number of internal nodes. The inclusion of internal nodes allow to recover the structure eigenmodes and makes feasible the coupling of the assembled systems with a surrounding environment, for instance, an acoustic field. The results obtained are compared with a standard Finite Element eigenvalue analysis. It is shown that for increasing response frequencies, the Boundary Element scheme delivers modal data within a degree of accuracy, which is only obtained by the conventional Finite Element Method with considerable finer meshes.     

An anisotropic linear elastic boundary element formulation for masonry wall analysis

This work presents an application of a Boundary Element Method (BEM) formulation for anisotropic body analysis using isotropic fundamental solution. The anisotropy is considered by expressing a residual elastic tensor as the difference of the anisotropic and isotropic elastic tensors. Internal variables and cell discretization of the domain are considered. Masonry is a composite material consisting of bricks (masonry units), mortar and the bond between them and it is necessary to take account of anisotropy in this type of structure. The paper presents the formulation, the elastic tensor of the anisotropic medium properties and the algebraic procedure. Two examples are shown to validate the formulation and good agreement was obtained when comparing analytical and numerical results. Two further examples in which masonry walls were simulated, are used to demonstrate that the presented formulation shows close agreement between BE numerical results and different Finite Element (FE) models.     

BEM Implementation of the Energy Domain Integral for the Elastoplastic Analysis of 3D Fracture Problems

An Elastoplastic Dual Boundary Element Method (EPDBEM) for the evaluation of the J-integral in three-dimensional fracture problems is presented in this paper. The point-wise J-integral is evaluated along crack fronts using the Energy Domain Integral (EDI) methodology. The domain expression of the EDI is naturally compatible with the EPDBEM, allowing to embed the computation of the J-integral within the boundary element formulation in such a way that it only accounts for a small additional computational effort. The accuracy of the proposed formulation is demonstrated by solving problems with straight and curved crack fronts. This revised version was published online in July 2006 with corrections to the Cover Date.     

Static boundary element analysis of piles submitted to horizontal and vertical loads

In this paper a numerical model for the analysis of the interaction between soil and piles, with or without rigid caps, subjected to horizontal and vertical loads is presented. The piles are modelled here by the Finite Element Method (FEM) and the soil by the Boundary Element Method (BEM). In this formulation the pile is represented as one finite element and the displacements and tractions along the shaft are approximated by polynomial functions. Some examples are presented and the results obtained with this formulation are very close to those obtained with other formulations and with experimental results.     

Boundary element method for finite elasticity

This paper describes some integral formulations and implementations of a Boundary Element Method to solve two- and three-dimensional finite deformation problems of rubber-like materials. The integral equations are formulated in terms of unknown incremental displacement and total boundary traction fields, or alternatively in terms of the incremental displacement and incremental boundary traction fields. The elastic material is either compressible or incompressible with given constitutive equations. Both formulations are implemented and tested. The uniaxial elongation and simple shear deformations of a model material are successfully simulated by both formulations. Some non-trivial examples are performed using the first formulation.     

A three-dimensional boundary element formulation for the elastoplastic analysis of cracked bodies

In this paper a general boundary element formulation for the three-dimensional elastoplastic analysis of cracked bodies is presented. The non-linear formulation is based on the Dual Boundary Element Method. The continuity requirements of the field variables are fulfilled by a discretization strategy that incorporates continuous, semi-discontinuous and discontinuous boundary elements as well as continuous and semi-discontinuous domain cells. Suitable integration procedures are used for the accurate integration of the Cauchy surface and volume integrals. The explicit version of the initial strain formulation is used to satisfy the non-linearity. Several examples are presented to demonstrate the application of the proposed method. © 1998 John Wiley & Sons, Ltd.     

TREATMENT OF BODY-FORCE VOLUME INTEGRALS IN BEM BY EXACT TRANSFORMATION FOR 2-D ANISOTROPIC ELASTICITY

In the Boundary Element Method (BEM) based on the direct formulation, body-force effects manifest themselves as an additional volume integral term in the Boundary Integral Equation (BIE). The numerical solution of the integral equation with this term destroys the notion of the BEM as atruly boundary solution method. This paper discusses the treatment of this volume integral for two-dimensional anisotropic elasticity with body-forces present. The analytical basis for transforming this integral exactly into boundary ones is presented for geometrically convex regions. This restores the application of the BEM to such problems as a truly boundary solution technique. Numerical examples are presented to demonstrate the veracity of the transformation and implementation. © 1997 by John Wiley & Sons, Ltd.     

Viscoplastic response and creep failure time prediction of polymers based on the transient network model

The nonlinear viscoelastic/viscoplastic response of polymeric materials is described by a new model based on previous works in terms of monotonic loading, stress–relaxation, and creep. In the proposed analysis, following a constitutive equation of viscoelasticity, based on the transient network theory, essential modifications are introduced, which account for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. In addition, viscoplastic response is successfully analyzed by a proper kinematic formulation, which is combined with a functional form of the rate of plastic deformation. A three-dimensional constitutive equation is then derived for an isotropic incompressible medium. This analysis is capable of capturing the main aspects of inelastic response and the instability stage taking place at the tertiary creep, related to the creep failure. Model simulations described successfully the experimental data of polypropylene, which were performed elsewhere.     

高层建筑—地基动力相互作用半解析法的研究

提出一种上部结构有限条法、地基（土）特解边界元法相结合的半解析方法，首次建立了这一力学模型在频域内的运动方程，并编制了求解结构－地基动力相互作用的程序。通过计算有关算例，并与ＳｕｐｅｒＳＡＰ程序计算结果进行比较，证明本文的基本理论和计算程序是正确、可行的。     

Revisited mixed-value method via symmetric BEM in the substructuring approach

Within the Symmetric Boundary Element Method, the mixed-value analysis is re-formulated. This analysis method contemplates the subdivision of the body into substructures having interface kinematical and mechanical quantities. For each substructure an elasticity equation, connecting weighted displacements and tractions to nodal displacements and forces of the same interface boundary and to external action vector, is introduced. The assembly of the substructures is performed through both the strong and weak regularity conditions of the displacements and tractions. We obtain the solving equations where the compatibility and the equilibrium are guaranteed in the domain Ω for the use of the fundamental solution and at the interface nodes for the strong regularity conditions imposed, whereas the previous quantities are respected in weighted form along the interface boundaries. The mixed-value method leads to a better solution than those obtained through the displacement method of the Symmetric Boundary Element Method, if compared with the analytical solution.By using the Karnak.sGbem program, developed with other researchers and updated through the implementation of the present method, some examples are made which show the advantages related to the computational aspects and to the convergence of the numerical response.     

The meshless hypersingular boundary node method for three-dimensional potential theory and linear elasticity problems

The Boundary Node Method (BNM) represents a coupling between Boundary Integral Equations (BIEs) and Moving Least Squares (MLS) approximants. The main idea here is to retain the dimensionality advantage of the former and the meshless attribute of the latter. The result is a ‘meshfree’ method that decouples the mesh and the interpolation procedures. The BNM has been applied to solve 2-D and 3-D problems in potential theory and linear elasticity. The Hypersingular Boundary Element Method (HBEM) has diverse important applications in areas such as fracture mechanics, wave scattering, error analysis and adaptivity, and to obtain a symmetric Galerkin boundary element formulation. The present work presents a coupling of Hypersingular Boundary Integral Equations (HBIEs) with MLS approximants, to produce a new meshfree method — the Hypersingular Boundary Node Method (HBNM). Numerical results from this new method, for selected 3-D problems in potential theory and in linear elasticity, are presented and discussed in this paper.     

Integral formulation to simulate the viscous sintering of a two-dimensional lattice of periodic unit cells

In this paper a mathematical formulation is presented which is used to calculate the flow field of a two-dimensional Stokes fluid that is represented by a lattice of unit cells with pores inside. The formulation is described in terms of an integral equation based on Lorentz's formulation, whereby the fundamental solution is used that represents the flow due to a periodic lattice of point forces. The derived integral equation is applied to model the viscous sintering phenomenon, viz. the process that occurs (for example) during the densification of a porous glass heated to such a high temperature that it becomes a viscous fluid. The numerical simulation is carried out by solving the governing Stokes flow equations for a fixed domain through a Boundary Element Method (BEM). The resulting velocity field then determines an approximate geometry at a next time point which is obtained by an implicit integration method. From this formulation quite a few theoretical insights can be obtained of the viscous sintering process with respect to both pore size and pore distribution of the porous glass. In particular, this model is able to examine the consequences of microstructure on the evolution of pore-size distribution, as will be demonstrated for several example problems.