久一郎 鷲津

Bio: 久一郎 鷲津 is an academic researcher. The author has contributed to research in topics: Elasticity (economics). The author has an hindex of 1, co-authored 1 publications receiving 193 citations.

Heritage and early history of the boundary element method

Abstract: This article explores the rich heritage of the boundary element method (BEM) by examining its mathematical foundation from the potential theory, boundary value problems, Green's functions, Green's identities, to Fredholm integral equations. The 18th to 20th century mathematicians, whose contributions were key to the theoretical development, are honored with short biographies. The origin of the numerical implementation of boundary integral equations can be traced to the 1960s, when the electronic computers had become available. The full emergence of the numerical technique known as the boundary element method occurred in the late 1970s. This article reviews the early history of the boundary element method up to the late 1970s.

Origin of band gaps in graphene on hexagonal boron nitride

Abstract: Graphene doesn’t usually have a bandgap but one can appear when the two-dimensional material is placed on a hexagonal boron nitride substrate. Jung et al. now develop a theory that indicates that this occurs because the graphene’s carbon atoms structurally relax when placed on boron nitride.

Buckling analysis and optimisation of variable angle tow composite plates

Abstract: Variable angle tow (VAT) placed composite laminates, where the fibre orientations continuously varying over the plane of each ply, generally exhibit variable stiffness properties. The stiffness tailoring of VAT plates through the design of fibre orientation distributions can substantially improve the buckling resistance, which is mainly due to the benign, non-uniform, in-plane load redistribution. In this work, a new mathematical definition is proposed to represent the general variation of fibre-orientation in the VAT plate. In this definition, the coefficients of polynomials are directly equal to the designed fibre angles at pre-selected control points. A Rayleigh–Ritz approach is used to determine the prebuckling loads distributions and critical buckling load of VAT plates. It provides a more efficient means to evaluate the buckling load of VAT laminates, compared with other numerical solutions. Subsequently, preliminary optimisation of VAT plates for maximum buckling load is done using the proposed definition of non-linear variation of fibre angles. Results obtained for simply supported square VAT plates are compared with optimal results reported in the literature. Finally, long VAT plates with one free edge and others simply supported are studied to demonstrate the viability of the proposed modelling strategy.

Recent Advances and Emerging Applications of the Boundary Element Method

Abstract: Sponsored by the U.S. National Science Foundation, a workshop on the boundary element method (BEM) was held on the campus of the University of Akron during September 1–3, 2010 (NSF, 2010, “Workshop on the Emerging Applications and Future Directions of the Boundary Element Method,” University of Akron, Ohio, September 1–3). This paper was prepared after this workshop by the organizers and participants based on the presentations and discussions at the workshop. The paper aims to review the major research achievements in the last decade, the current status, and the future directions of the BEM in the next decade. The review starts with a brief introduction to the BEM. Then, new developments in Green's functions, symmetric Galerkin formulations, boundary meshfree methods, and variationally based BEM formulations are reviewed. Next, fast solution methods for efficiently solving the BEM systems of equations, namely, the fast multipole method, the pre-corrected fast Fourier transformation method, and the adaptive cross approximation method are presented. Emerging applications of the BEM in solving microelectromechanical systems, composites, functionally graded materials, fracture mechanics, acoustic, elastic and electromagnetic waves, time-domain problems, and coupled methods are reviewed. Finally, future directions of the BEM as envisioned by the authors for the next five to ten years are discussed. This paper is intended for students, researchers, and engineers who are new in BEM research and wish to have an overview of the field. Technical details of the BEM and related approaches discussed in the review can be found in the Reference section with more than 400 papers cited in this review.

A variational principle for the formulation of partitioned structural systems

Abstract: A continuum-based variational principle is presented for the formulation of the discrete governing equations of partitioned structural systems. This application includes coupled substructures as well as subdomains obtained by mesh decomposition. The present variational principle is derived by a series of modifications of a hybrid functional originally proposed by Atluri for finite element development. The interface is treated by a displacement frame and a localized version of the method of Lagrange multipliers. Interior displacements are decomposed into rigid-body and deformational components to handle floating subdomains. Both static and dynamic versions are considered. An important application of the present principle is the treatment of nonmatching meshes that arise from various sources such as separate discretization of substructures, independent mesh refinement, and global–local analysis. The present principle is compared with that of a globalized version of the multiplier method. Copyright © 2000 John Wiley & Sons, Ltd.