Boundary-element parallel-computing algorithm for the microstructural analysis of general composites.

A standard continuum-mechanics-based 3D boundary-element (BE) algorithm has been devised to the microstructural modeling of complex heterogeneous solids such as general composites. In the particular applications of this paper, the mechanical properties of carbon-nanotube?reinforced composites are estimated from three-dimensional representative volume elements (RVEs). The shell-like thin-walled carbon nanotubes (CNTs) are also simulated with 3D BE models, and a generic subregion-by-subregion (SBS) algorithm makes the microstructural description of the CNT?polymer systems possible. In fact, based on this algorithm, a general scalable BE parallel code is proposed. Square and hexagonal fiber-packing patterns are considered to simulate the 3D composite microstructures

Simulation of flash-butt welding process of a railway steel. Part 1 : residual stress analysis via FEM.

Trilhos longos, soldados pelo processo Flash Butt Welding (FBW), s?o a realidade das ferrovias brasileiras de m?dia e alta carga por eixo. Embora apresentem caracter?sticas desej?veis do ponto de vista do comportamento din?mico da via, as soldas s?o regi?es de descontinuidade estrutural e mec?nica onde se originam tens?es residuais, e que est?o associadas a falhas prematuras por fadiga. Simula??es num?ricas termomec?nicas, fisicamente n?o-lineares, no dom?nio do tempo, pelo M?todo dos Elementos Finitos (MEF), foram empregadas para avaliar o desenvolvimento de tens?es residuais originadas durante o processo de soldagem. Uma nova abordagem para a inclus?o do aporte de calor envolvido no processo ? proposta. Os resultados num?ricos s?o comparados a medidas experimentais de tens?es residuais superficiais e aspectos macrogr?ficos das juntas, incluindo largura da Zona Termicamente Afetada (ZTA) e dados de taxas de resfriamento. Os resultados mostram boa correla??o entre as an?lises num?ricas e medidas experimentais de tens?es residuais. Aspectos fundamentais relacionados ao desenvolvimento de tens?es residuais s?o esclarecidos a partir da correla??o entre an?lises num?rica e experimental. Ademais, verifica-se que os modelos computacionais podem ser utilizados na previs?o de pontos cr?ticos para nuclea??o de trincas por fadiga e/ou avaliar efeitos de vari?veis de processo sobre o campo de tens?es residuais.Long rails, welded by the Flash-Butt Welding (FBW) process, are the reality of the Brazilian railroads for medium and high axle loads. Although they present desirable characteristics concerning the dynamic behavior of the track, welded joints are regions of structural and mechanical discontinuity where high residual stresses originate, and, consequently, premature fatigue failures may take place. This paper employs the Finite Element Method (FEM) to carry out transient, physically non-linear thermo-mechanical analyses to evaluate residual stresses evolved in the welding process. A new approach is proposed to take into account the heat input involved in the process. The numerical results are compared to experimentally measured surface residual stresses, and to the macrographic joint aspects, including the HAZ width and cooling rate data. The results show a good correlation between the numerical and experimental measurements of residual stresses. Fundamental aspects related to the development of residual stresses are clarified, correlating numerical and experimental analyses. In addition, it is verified that the computational models can be used to predict critical crack nucleation points by fatigue, and/or to evaluate effects of process parameters on the residual stress field

Analysis of thin-walled structural elements via 3D standard BEM with generic substructuring.

This paper is concerned with the application of standard 3DBoundary Element Methods to solve thin-walled structural elements (needle-like/shell-like solids). A subregion- by-subregion data structure, incorporating iterative solvers and discontinuous boundary elements, is presented. To efficiently and accurately evaluate the quasi-singular integrals, special quadrature methods are applied. In addition, structured matrix-vector products, designed to avoid the excessive number of conditional tests during solver iterations, are proposed. Numerical results for complex thinwalled BE models are validated by comparison with FEM calculations and previously published BEM analyses

An explicit direct FEM?BEM coupling procedure for nonlinear dynamics.

In this work, an explicit direct FEM?BEM coupling procedure is proposed for nonlinear dynamics. In this procedure, each subdomain of the model is analysed separately taking into account proper interface conditions, allowing optimized solver procedures to be applied within each subdomain. In addition, the solution procedure is carried out directly (i.e., without any iterative process), since an explicit time-marching technique is employed within the FEM subdomains. In this context, a locally stabilized central difference approach is utilized, ensuring stability for the FEM analyses, as well as enhanced accuracy. Thus, a very efficient and versatile coupled solution takes place, allowing the direct and independent solution of the subdomains of the model, without regarding critical time-steps limitations within the explicit subdomains. A multi-level time-step algorithm is also considered here, enabling different time-steps to be applied to each subdomain of the model, further improving the flexibility of the coupled analyses. At the end of the paper, numerical applications are presented, illustrating the effectiveness and versatility of the proposed methodology

Boundary-integral-based process for calculating stiffness matrices of space frame elements with axially varying cross section.

This paper presents a strategy to directly compute the stiffness matrix of 3D (space) frame elements having arbitrary cross sections and generic rigidity variation along their axes. All the necessary section properties are determined by means of formulations based purely on boundary integrals. To determine the torsional constant and the torsion center, this strategy applies the Boundary Element Method (BEM). To model thin-walled crosssections, the strategy calls for activating integration algorithms devised specifically to deal with the nearly singular integrals involved. To express all other section properties (i.e. area, first and second moments of area, and the shear form factors) in terms of boundary integrals, the strategy employs Green's theorem. The existing boundary-element meshes, used to determine the torsion constants, are employed to evaluate the corresponding boundary integrals. In applying the proposed strategy ? the pure boundary-integral-based process (PBIP) ? we consider space frame elements with geometrically complex cross-sections varying along their axes

Revisiting the BE SBS algorithm and applying it to solve torsion problems in composite bars : robustness and efficiency study.

The construction of truly competitive boundary-element (BE) codes, capable of analyzing real-life engineering problems, unavoidably requires the devising of coupling strategies to make the modeling of complex heterogeneous domains user-friendly. Thereby, high-performance algorithms for solving the highly sparse resulting system of equations are essential. Moreover, as discontinuous boundary elements are necessary to alleviate the modeling process of coupled domains, efficient (low-order) quadratures for integrating singular and nearly-singular fundamental kernels over the boundary elements must be implemented. This paper newly discusses the construction of the boundary-element subregion-by-subregion (BE SBS) technique based on a BEM formulation for torsion problems in general composite bars. One also presents details of the formulation of the Krylov solvers BiCG and BiCGSTAB-(l), embedded in the coupling algorithm. In addition, the BE SBS matrix structure itself is used to form an efficient sparse incomplete LU factorization (SILU) preconditioner to accelerate the iterative solution process. Torsion problems in bars with complex composite patterns (e.g. with many different materials) are analyzed to attest the efficiency and robustness of the whole boundary-element technique

Geometric nonlinear analysis of plane frames with generically nonuniform shear-deformable members.

This paper employs the Direct Stiffness Method (DSM) to carry out geometric nonlinear analysis of plane frames with nonuniform physical-geometric characteristics. At the element level, a flexibility system of equations based on the principle of virtual forces (PVF) is established to calculate the tangent stiffness matrix and the equivalent nodal loads. The formulation allows for the easy modeling of shear-deformable frame elements with generic rigidity variation along their axes. In addition, Green's theorem is considered to express all the necessary section properties in terms of boundary integrals. This considerably simplifies the modeling of complex cross sections of arbitrary shapes. A ?boundary-element? mesh is then used to model the geometric description of the cross sections. At the structure level, to determine the nonlinear equilibrium trajectories for the frame, we apply a co-rotational updated Lagrangian formulation along with an incremental-iterative full Newton-Raphson process. Large displacements and internal member forces are accurately reconstituted. Frameworks having elements with geometrically complex cross-sections varying along their axes are analyzed to validate the strategy proposed

Generic domain decomposition and iterative solvers for 3D BEM problems.

In the past two decades, considerable improvements concerning integration algorithms and solvers involved in boundary-element formulations have been obtained. First, a great deal of efficient techniques for evaluating singular and quasi-singular boundary-element integrals have been, definitely, established, and second, iterative Krylov solvers have proven to be advantageous when compared to direct ones also including non-Hermitian matrices. The former fact has implied in CPU-time reduction during the assembling of the system of equations and the latter fact in its faster solution. In this paper, a triangle-polar-co-ordinate transformation and the Telles co-ordinate transformation, applied in previous works independently for evaluating singular and quasi-singular integrals, are combined to increase the efficiency of the integration algorithms, and so, to improve the performance of the matrixassembly routines. In addition, the Jacobi-preconditioned biconjugate gradient (J-BiCG) solver is used to develop a generic substructuring boundary-element algorithm. In this way, it is not only the system solution accelerated but also the computer memory optimized. Discontinuous boundary elements are implemented to simplify the coupling algorithm for a generic number of subregions. Several numerical experiments are carried out to show the performance of the computer code with regard to matrix assembly and the system solving. In the discussion of results, expressed in terms of accuracy and CPU time, advantages and potential applications of the BE code developed are highlighted

Application of a generic domain-decomposition strategy to solve shell-like problems through 3D BE models.

Efficient integration algorithms and solvers specially devised for boundary-element procedures have been established over the last two decades. A good deal of quadrature techniques for singular and quasisingular boundary-element integrals have been developed and reliable Krylov solvers have proven to be advantageous when compared to direct ones, also in case of non-Hermitian matrices. The former has implied in CPU-time reduction during the assembling of the system of equations and the latter in its faster solution. Here, a triangular polar co-ordinate transformation and the Telles co-ordinate transformation are employed separately and combined to develop the matrix-assembly routines (integration routines). In addition, the Jacobi-preconditioned Biconjugate Gradient solver (J-BiCG) is used along with a generic substructuring boundary element algorithm. Thus, solution CPU time and computer memory can be considerably reduced. Discontinuous boundary elements are also included to simplify the coupling of the BE models (substructures). Numerical experiments involving 3D thin-walled domains (shell-like structural elements) are carried out to show the performance of the computer code with respect to accuracy and efficiency of the system solution. Precision, CPU-time and potential applications of the BE code developed are commented upon

A robustness-based design strategy for composite structures ? probabilistic approach.

Purpose ? The purpose of this paper is to present the probabilistic approach to a new robustness-based design strategy for thin-walled composite structures in post-buckling. Design/methodology/approach ? Because inherent uncertainties in geometry, material properties, ply orientation and thickness affect the structural performance and robustness, these variations are taken into account. Findings ? The methodology is demonstrated for the sake of simplicity with an unstiffened composite plate under compressive loading, and the probabilistic and deterministic results are compared. In this context, the structural energy and uncertainties are employed to investigate the robustness and reliability of thin-walled composite structures in post-buckling. Practical implications ? As practical implication, the methodology can be extended to stiffened shells, widely used in aerospace design with the aim to satisfy weight, strength and robustness requirements. Moreover, a new argument is strengthened to accept the collapse close to ultimate load once robustness is ensured with a required reliability. Originality/value ? This innovative strategy embedded in a probabilistic framework might lead to a different design selection when compared to a deterministic approach, or an approach that only accounts for the ultimate load. Moreover, robustness measures are redefined in the context of a probabilistic design