Nonlinear IGABEM formulations for the mechanical modelling of 3D reinforced structures

Analysis of 2D contact problems under cyclic loads using IGABEM with Bézier decomposition

“…The Isogeometric Boundary Element Method (IGABEM) was first proposed by [17,18] and its formulation has the capability of integrating CAD and numerical analysis, enhancing the design process. It has been successfully applied in many instances: [19] extended the formulation for three-dimensional analysis, [20] used hierarchical matrix to reduce the computational cost of the method, [21] used the IGABEM to analyse problems in automotive acoustics, [22] applied the isogeometric analysis accelerated by fast multipole method to analyse twodimensional potential problems, [23] applied IGABEM for topology optimisation, [24] simulated inclusions and reinforcement bars, [25] extended the method for thermo-elasticity, and [26] used IGABEM for modelling 3D reinforced structures. A comprehensive reference for IGABEM can be found in [27].…”

IGA-Energetic BEM: An Effective Tool for the Numerical Solution of Wave Propagation Problems in Space-Time Domain

“…In fact, from one side, BEM needs to work only on the boundary of the problem domain, hence avoiding domain meshing, and, from the other, IGA uses the same B-spline or NURBS basis, as adopted in CAD systems, to describe both the boundary and the approximate solution of the problem at hand, drastically reducing the number of degrees of freedom (DoFs) and giving surprising computational advantages with regard to the classical Lagrangian basis. In the last 10 years, IGA-BEM has been fruitfully applied to a variety of elliptic problems reformulated in terms of Boundary Integral Equations (BIEs), such as the Laplace equation [3][4][5][6][7][8][9][10][11][12][13], Helmholtz equation [9,[13][14][15][16], elastostatics, and crack problems [17][18][19][20][21]; on the other hand, little attention has been devoted to the numerical solution of differential problems in time domains (see [22][23][24] as very recent works in this context).…”

Numerical formulations based on the Isogeometric Boundary Element Method for the mechanical analysis of three-dimensional reinforced nonhomogeneous solids

“…Finally, several contributions in the field of three-dimensional IGABEM formulations have been made, highlighting the non-homogeneous reinforced domains modelling, fracture mechanics, nonlinear formulations and adaptive mesh refinement. Besides, three papers were published (132,182,183) with the advances made in this thesis.…”

“… tH (7.32) where K 1DBEM and G 1DBEM are the 1DBEM influence matrices (182). K FEM and G FEM are the classical stiffness matrix and lumping matrix, respectively, from the truss FEM formulation.…”