Nitsche's method method for mixed dimensional analysis: conforming and non-conforming continuum-beam and continuum-plate coupling

Abstract

A Nitche's method is presented to couple different mechanical models. They include coupling of a solid and a beam and of a solid and a plate. Both conforming and non-conforming formulations are presented. In a non-conforming for- mulation, the structure domain is overlapped by a refined solid model. Applications can be found in multi-dimensional analyses in which parts of a structure are modeled with solid elements and others are modeled using a coarser model with beam and/or plate elements. Discretisations are performed using both standard Lagrange elements and high order NURBS (Non Uniform Rational Bsplines) based isogeometric elements. We present various examples to demonstrate the performance of the method.

Figures (34)

• Figure 1: Solid-structure coupling: (a) conforming coupling and (b) non-conforming coupling. The bold lines represent the coupling line/surface.
• Figure 2: Coupling of a two dimensional solid and a beam.
• Figure 3: Coupling of a three dimensional solid and a plate.
• Figure 4: Quadratic B-spline basis functions defined for the open, non-uniform knot vector $\Xi=\{0,0,0,1,2,3,4,4,5,5,5\}$. Note the flexibility in the construction of basis functions with varying degrees of regularity.
• Figure 5: Diagrammatic interpretation of mappings from parent space ($\tilde{\Omega}$) through parametric space ($\hat{\Omega}$) to physical space ($\Omega$). The parent space is where numerical quadrature rules are defined.

Theorems & Definitions (4)

• Remark 4.1
• Remark 4.2
• Remark 5.1
• Remark 6.1