International Journal for Numerical Methods in Engineering

doi: 10.1002/nme.5013pmid: N/A

No abstract is available for this article.

doi: 10.1002/nme.5014pmid: N/A

No abstract is available for this article.

Shivanian, Elyas

doi: 10.1002/nme.4960pmid: N/A

Summary In this article, the meshless local radial point interpolation method is applied to analyze three space dimensional wave equations of the form utt+αut+βu=uxx+uyy+uzz+f(x,y,z,t),xT=(x,y,z)∈Ω⊆Rd,(d=2,3),t>0 subject to given initial and Dirichlet boundary conditions. The main difficulty of the great number of methods in full 3‐D problems is the large computational costs. In meshless local radial point interpolation method, it does not require any background integration cells, so that all integrations are carried out locally over small quadrature domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions. The point interpolation method with the help of radial basis functions is proposed to construct shape functions that have Kronecker delta function property. A weak formulation with the Heaviside step function converts the set of governing equations into local integral equations on local subdomains. A two‐step time discretization method is employed to evaluate the time derivatives. This suggests Crank‐Nicolson technique to be applied on the right hand side of the equation. The convergence analysis and stability of the method are fully discussed. Three illustrative examples are presented, and satisfactory agreements are achieved. It is shown theoretically that the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones. Copyright © 2015 John Wiley & Sons, Ltd.

Terada, Kenjiro; Hirayama, Norio; Yamamoto, Koji; Muramatsu, Mayu; Matsubara, Seishiro; Nishi, Shin‐nosuke

doi: 10.1002/nme.4970pmid: N/A

Summary A method of numerical plate testing (NPT) for composite plates with in‐plane periodic heterogeneity is proposed. In the two‐scale boundary value problem, a thick plate model is employed at macroscale, while three‐dimensional solids are assumed at microscale. The NPT, which is nothing more or less than the homogenization analysis, is in fact a series of microscopic analyses on a unit cell that evaluates the macroscopic plate stiffnesses. The specific functional forms of microscopic displacements are originally presented so that the relationship between the macroscopic resultant stresses/moments and strains/curvatures to be consistent with the microscopic equilibrated state. In order to perform NPT by using general‐purpose FEM programs, we introduce control nodes to facilitate the multiple‐point constraints for in‐plane periodicity. Numerical examples are presented to verify that the proposed method of NPT reproduces the plate stiffnesses in classical plate and laminate theories. We also perform a series of homogenization, macroscopic, and localization analyses for an in‐plane heterogeneous composite plate to demonstrate the performance of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

Florentie, Liesbeth; Blom, David S.; Scholcz, Thomas P.; Zuijlen, Alexander H.; Bijl, Hester

doi: 10.1002/nme.4979pmid: N/A

Summary Fluid–structure interactions (FSI) play a crucial role in many engineering fields. However, the computational cost associated with high‐fidelity aeroelastic models currently precludes their direct use in industry, especially for strong interactions. The strongly coupled segregated problem—that results from domain partitioning—can be interpreted as an optimization problem of a fluid–structure interface residual. Multi‐fidelity optimization techniques can therefore directly be applied to this problem in order to obtain the solution efficiently. In previous work, it is already shown that aggressive space mapping (ASM) can be used in this context. In this contribution, we extend the research towards the use of space mapping for FSI simulations. We investigate the performance of two other approaches, generalized space mapping and output space mapping, by application to both compressible and incompressible 2D problems. Moreover, an analysis of the influence of the applied low‐fidelity model on the achievable speedup is presented. The results indicate that output space mapping is a viable alternative to ASM when applied in the context of solver coupling for partitioned FSI, showing similar performance as ASM and resulting in reductions in computational cost up to 50% with respect to the reference quasi‐Newton method. Copyright © 2015 John Wiley & Sons, Ltd.