Analysis of 3D time-dependent acoustic problems via a generic BE substructuring algorithm based on iterative solvers.

In this paper, a generic BE/BE coupling algorithm based on iterative solvers is applied to solve 3D time-dependent acoustic problems. As regards the treatment of the time-dependence, a direct time-marching scheme is considered. Several types of boundary elements and cells are available in the code for the spatial description of the involved variables. Concerning the BE/BE coupling technique, its chief idea is to completely avoid storing and manipulating the zero blocks appearing in the coupled system by the use of iterative solvers. The global system matrix is not explicitly assembled; instead the algebraic subsystems (associated with the substructures of the model) are manipulated as they were independent of each other. An insight into the coupling strategy and the used iterative solver (Jacobi-preconditioned bi-conjugate gradient method) is given. Analyses of sound barriers are carried out for verifying the performance of the respective computational code modules

An efficient BE iterative-solver-based substructuring algorithm for 3D time-harmonic problems in elastodynamics.

This work is concerned with the development of an efficient and general algorithm to solve frequency-domain problems modelled by the boundary element method based on a sub-region technique. A specific feature of the algorithm discussed here is that the global sparse matrix of the coupled system is implicitly considered, i.e. problem quantities are not condensed into interface variables. The proposed algorithm requires that only the block matrices with non-zero complex-valued coefficients be stored and manipulated during the analysis process. In addition, the efficiency of the technique presented is improved by using iterative solvers. The good performance of pre-conditioned iterative solvers for systems of equations having real-valued coefficients, well demonstrated in the literature, is confirmed for the present case where the system matrix coefficients are complex. The efficiency of the algorithm described here is verified by analysing a soil–machine foundation interaction problem. CPU time and accuracy are the parameters used for estimating the computational efficiency

Constructing efficient substructure-based preconditioners for BEM systems of equations?

In this work, a generic substructuring algorithm is employed to construct global block-diagonal preconditioners for BEM systems of equations. In this strategy, the allowable fill-in positions are those on-diagonal block matrices corresponding to each BE subregion. As these subsystems are independently assembled, the preconditioner for a particular BE model, after the LU decomposition of all subsystem matrices, is easily formed. So as to highlight the efficiency of the preconditioning proposed, the Bi-CG solver, which presents a quite erratic convergence behavior, is considered. In the particular applications of this paper, 3D representative volume elements (RVEs) of carbon-nanotube (CNT) composites are analyzed. The models contain up to several tens of thousands of degrees of freedom. The efficiency and relevance of the preconditioning technique is also discussed in the context of developing general (parallel) BE codes

New developments on BE/BE multi-zone algorithms based on krylov solvers - applications to 3D frequency-dependent problems.

In this paper, new developments concerning the use of BE/BE coupling algorithms for solving 3D time-harmonic problems are reported. The algorithms are derived by considering different iterative solvers. Their chief idea is to work with the global sparse matrix of the coupled system, however without considering the many zero blocks associated with the non-coupled nodes of different subregions. The use of iterative solvers makes it possible to store and manipulate only the block matrices with non-zero coefficients. Preconditioned iterative solvers based on the Lanczos, bi-conjugate gradient, and GMRES (generalized minimal residual) methods are used to derive the BE/BE coupling algorithms. A description of the formulation of these solvers, which are completely general and can be applied to any non-singular, non-hermitian systems of equations, is provided. The performance of the algorithms is verified by solving some foundation-soil interaction problems. Important parameters for estimating the efficiency of the algorithms as required CPU times, matrix sparsity, and accuracy of the obtained responses are presented in the results of the paper

On the use of pseudo-forces to consider initial conditions in 3D time- and frequency-domain acoustic analysis.

This work is mainly concerned with a general strategy, based on well known concepts of classical mechanics, for taking into account initial conditions in frequency-domain (FD) and time-domain (TD) analyses. A general approach, extended here to three-dimensional applications, is presented. Special problems associated with analyses through Discrete-Fourier-Transform (DFT) algorithms, as those occurring in consequence of a non-correct choice of extended period or those connected with aliasing phenomenon, are also discussed. Furthermore, an alternative starting procedure for time-marching schemes (in TD analyses) is proposed. At the end of the paper, to validate the proposed techniques and to demonstrate their generality, two- and three-dimensional problems with non-homogeneous initial conditions are solved through frequency- and time-domain approaches by employing the Finite Element Method (FEM). Numerical results are compared with existing analytical solutions

A Robustness-Based Design Strategy for Composite Structures

Purpose – This paper aims to present a new robustness-based design strategy for thin-walled composite structures under compressive loading, which combines strength requirements in terms of the limit and ultimate load with robustness requirements evaluated from the structural energy until collapse. Design/methodology/approach – In order to assess the structural energy, the area under the load-shortening curve between several characteristic points such as local buckling, global buckling, onset of degradation and collapse load is calculated. In this context, a geometrically nonlinear finite element analysis is carried out, in which the ply properties are selectively degraded by progressive failure. Findings – The advantage of the proposed methodology is observed by analyzing unstiffened composite plates under compressive loading, wherein the lightest plate that satisfies both strength and robustness requirements can be attained. Practical implications – As a practical implication, this methodology gives a new argument to accept the collapse load close to the ultimate load once robustness is ensured. Originality value – The structural energy is employed to investigate the robustness of thin-walled composite structures in postbuckling, and new energy-based robustness measures are proposed. In the design of composite structures, this innovative strategy might lead to a more robust design when compared to an approach that only accounts for the ultimate load

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