Mirza Cenanovic

Mirza Cenanovic, Peter Hansbo, Mats G. Larson

We construct a cut finite element method for the membrane elasticity problem on an embedded mesh using tangential differential calculus. Both free membranes and membranes coupled to 3D elasticity are considered. The discretization comes from a Galerkin method using the restriction of 3D basis funtions (linear or trilinear) to the surface representing the membrane. In the case of coupling to 3D elasticity, we view the membrane as giving additional stiffness contributions to the standard stiffness matrix resulting from the discretization of the three-dimensional continuum.

Mirza Cenanovic, Peter Hansbo, Mats G. Larson

In this paper we consider finite element approaches to computing the mean curvature vector and normal at the vertices of piecewise linear triangulated surfaces. In particular, we adopt a stabilization technique which allows for first order $L^2$-convergence of the mean curvature vector and apply this stabilization technique also to the computation of continuous, recovered, normals using $L^2$-projections of the piecewise constant face normals. Finally, we use our projected normals to define an adaptive mesh refinement approach to geometry resolution where we also employ spline techniques to reconstruct the surface before refinement. We compare or results to previously proposed approaches.

Sudip Kumar Das, Mirza Cenanovic, Junfeng Zhang

In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami operator approach in the literature. This work, in addition to providing an alternative expression to calculate the mean curvature normal vector, can be further extended to other mesh structures, including non-triangular and heterogeneous meshes.

Mirza Cenanovic, Peter Hansbo, David Samvin

In this paper we suggest two modified one-point Gauss integration rules for the Q1 bi- or trilinear element. The modifications both stabilize the hourglass modes of the one-point rule, and one of them is accurate also on severely distorted elements. We investigate the performance of the integration rules for the hexahedron element, and combine standard one-point integration of the volumetric terms with the modified rules for the isochoric terms to handle near incompressible situations.

Mirza Cenanovic

We consider Trace finite element methods for the linear membrane problem on second order tetrahedral elements. To accomplish this, zero-level set reconstruction methods for second order tetrahedra are considered. For the higher order membrane model a corresponding stabilization is proposed and numerically evaluated. We compare combinations of background- and surface element order and provide numerical convergence results. The impact of the stabilization on the resulting solution is numerically analyzed. We also compare the choice of level set function with respect to the geometrical distance and normal errors.