Roger Andrew Sauer

This study employs the Finite Element Model Updating (FEMU) method for identification of material parameters and pretensioning forces in heterogeneous planar Bernoulli–Euler beams, which are analyzed using isogeometric analysis. The unknown material fields are discretized with a separate mesh based on Lagrange interpolation, referred to as the material mesh. The nodal values of the material mesh and the pretensioning force become discrete unknowns of the inverse problem. The FEMU objective function is formulated as a least‐square error, consisting of the differences between experimental and finite element displacements obtained from quasi‐static nonlinear calculations. To solve this problem, the Trust Region Interior Reflective algorithm is used. In addition, analytical derivatives are provided to accelerate the computations. The proposed approach is verified by the example of identifying Young's modulus distribution and pretensioning based on artificially generated experimental data. Results show that the material parameter identification is sensitive to noise. However, with sufficient experimental data, the influence of noise can be significantly reduced. The pretensioning force can be robustly reconstructed even for high noise levels.

A new arbitrary Lagrangian–Eulerian (ALE) formulation for Navier–Stokes flow on self-evolving surfaces is presented. It is based on a general curvilinear surface parameterisation that describes the motion of the ALE frame. Its in-plane part becomes fully arbitrary, while its out-of-plane part follows the material motion of the surface. This allows for the description of flows on deforming surfaces using only surface meshes. The unknown fields are the fluid density or pressure, the fluid velocity and the surface motion, where the latter two share the same normal velocity. The corresponding field equations are the continuity equation or area-incompressibility constraint, the surface Navier–Stokes equations and suitable surface mesh equations. Particularly advantageous are mesh equations based on membrane elasticity. The presentation focuses on the coupled set of strong and weak form equations, and presents several manufactured steady and transient solutions. These solutions are used together with numerical simulations to illustrate and discuss the properties of the proposed new ALE formulation. They also serve as basis for the development and verification of corresponding computational methods. The new formulation allows for a detailed study of fluidic membranes such as soap films, capillary menisci and lipid bilayers.