Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries

A parameter-free variational coupling approach for trimmed isogeometric thin shells

“…For optimal performance of the method, α needs to be chosen as small as possible. Element-wise configuration dependent stabilization parameters can be estimated based on a local eigenvalue problem [40,7,43,44]. The particular method (19) makes use of one-sided inequalities to establish estimates of local stabilization parameters.…”

“…Integrated design-through-analysis workflows for thin shell structures described by trimmed NURBS surfaces can be based on the combination of concepts from isogeometric analysis and embedded domain methods. In this context, we identify four key components [5][6][7][8][9] 1. ability to query geometric information related to trimmed surfaces from CAD data structures, 2. efficient and accurate isogeometric shell technology, 3. quadrature methods for the integration of stiffness and residual forms in trimmed elements, 4. methods to enforce boundary and coupling conditions at non-matching trimming curves.…”

Essential boundary and interface conditions in the meshless analysis of shells.

“…For the essential boundary we can obtain if δu = 0 , n n = n 1n An interesting approach is taken by [49] for enforcing EBCs, where the normal and tangential stress components are taken separately and have di erent parameters de ned in two separate local eigenproblems. Similar approach is taken in [50] for isogeometric analysis of patched geometries, where the local eigenproblem is used to estimate the stabilization over the interfaces.…”

“…The Finite Cell method consists of using FEs with spline base functions in a background mesh with immersed boundaries. Nitsche's method is than used to impose EBCs [49] and ICs [50] in two and three dimensional elasticity and is successful used to describe thin and solid-like shells [22,21,23] This chapter focus on modi cations of the weak form to impose EBCs and ICs between pairs of approximation domains in a shell model framework, retaining the MLS approximant in its most usual form for each domain. The next sections present the development needed for each type of modi cation of the weak form, recovering the original strong form whenever possible.…”

“…It has been applied with eXtended Finite Elements (XFEM) for EBCs and ICs in single-eld problems [15,25,28], to enforce weak discontinuities between elastic materials [51,52,2,1]; and applied to non conforming embedded FE meshes for elastostatics [53,54]. B-splines and NURBs-base FEs share similar features with meshless approximations and can also take advantage of Nitsche's Method, as in [16] for 2nd and 4th order problems, [46,33,49,50] for elasticity, [27,26] for thin plates and [22,23] for thin shells. The theory has also been extended for contact with FEs [59] and XFEM [4,3].…”