An isogeometric boundary element approach for topology optimization using the level set method

A NURBS-discontinuous and enriched isogeometric boundary element formulation for two-dimensional fatigue crack growth

“…8πµ (1 − ν) Regarding the TBIE, the kernel D em kij (22) can be evaluated in a similar manner to P em ij since both have the same order of singularity O(r −1 ). For S em kij (21), it can be firstly rewritten as: The SSM can also be used to evaluate the enriched kernels P eλ iM and Seλ ijM for elements containing the source point. In this case, the equations obtained are similar to Eqs.…”

“…In these works, the term IGABEM was coined for the numerical approach. The use of the IGABEM has since expanded, and the method has been applied to several problems involving geomechanics [14,15], acoustics [16][17][18], shape optimization [19][20][21], potential flow [22,23], heat transfer [24] and fracture [25][26][27][28]. Additionally, studies concerning the accurate evaluation of the singular and near-singular integrals arising in IGABEM can be found in [29][30][31].…”

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].…”

A coupled meshless element-free Galerkin and radial basis functions method for level set-based topology optimization

“…The available procedures optimize the given objective function under different constraints, e.g., the minimum compliance with optimal distribution of the given material within the design domain, [6,7]. Numerous numerical procedures including: homogenization method [8][9][10], solid isotropic material with penalization (SIMP) method [11], evolutionary structural optimization (ESO) [12], bi-directional ESO [13], and level set based optimization methods [14][15][16][17] have been reported, with each one have its own merits and de-merits. The TO based procedures have high end applications in various design and engineering processes as described in details in [18].…”