A surface oriented solid formulation based on a hybrid Galerkin-collocation method

The contribution is concerned with a numerical method to analyze the mechanical behavior of 3D solids. The method employs directly the geometry defined by the boundary representation modeling technique, which is frequently used in CAD to define solids. It combines the benefits of the isogeometric analysis methodology with the scaled boundary finite element method. In the present approach, only the boundary surfaces of the solid are discretized. No tensor-product structure of three-dimensional objects is exploited to parametrize the physical domain. The weak form is applied only on the boundary surfaces. The governing partial differential equations of elasticity are transformed to an ordinary differential equation (ODE) of Euler type. The isogeometric Galerkin approach is employed to approximate the displacement response at the boundary surfaces. It exploits the two-dimensional NURBS objects to parametrize the boundary surfaces. To solve the Euler type ODE, the NURBS based collocation approach is applied. The accuracy of the method is validated against the analytical solutions. The presented method is able to analyze solids, which are bounded by an arbitrary number of surfaces. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Desch‐Schappacher perturbation of one‐parameter semigroups on locally convex spaces

We prove a Desch‐Schappacher type perturbation theorem for strongly continuous and locally equicontinuous one‐parameter semigroups which are defined on a sequentially complete locally convex space.     

Multiscale damage analyis for steel structures

An approach to model the deterioration of steel structures is presented by transferring the results of a continuum damage mechanics analysis to an extended beam model which can account for the loss of structural integrity. Damage starts at the microscopic level by the initiation, growth and coalescence of voids with decreasing material resistance followed by the formation of microcracks at the mesoscale. Nevertheless, the material behavior can be sufficiently modelled on a phenomenological basis taking into account viscoplasticity, hardening effects and damage evolution. The associated model parameters are identified with the help of an evolutionary algorithm adapting numerical to experimental results. Using the finite element method a nonlocal formulation of the damage variable is required to obtain mesh-independent results by structural analysis. The maximum element size is limited by the small magnitude of the internal length. Therefore, numerical analyses of large scale 3D steel structures are computationally expensive. To reduce the effort a beam element is proposed to account for the plastic hinges and the loss of resistance in the course of damage evolution. The corresponding relationship of bending moment and curvature bases on the continuum damage mechanics model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundary concentrated finite elements for optimal boundary control problems of elliptic PDEs

We investigate the discretization of optimal boundary control problems for elliptic equations on two-dimensional polygonal domains by the boundary concentrated finite element method. We prove that the discretization error ||u^*-u_h^*||_L²(G)\|u^{*}-u_{h}^{*}\|_{L^{2}(\Gamma)} decreases like N ⁻¹, where N is the total number of unknowns. This makes the proposed method favorable in comparison to the h-version of the finite element method, where the discretization error behaves like N ^−3/4 for uniform meshes. Moreover, we present an algorithm that solves the discretized problem in almost optimal complexity. The paper is complemented with numerical results.     

Advanced finite element formulations for modeling thin piezoelectric structures

This contribution is concerned with mixed finite element formulations for modeling piezoelectric beam and shell structures. Due to the electromechanical coupling, specific deformation modes are joined with electric field components. In bending dominated problems incompatible approximation functions of these fields cause incorrect results. These effects occur in standard finite element formulations, where interpolation functions of lowest order are used. A mixed variational approach is introduced to overcome these problems. The mixed formulation allows for a consistent approximation of the electromechanical coupled problem. It utilizes six independent fields and could be derived from a Hu-Washizu variational principle. Displacements, rotations and the electric potential are employed as nodal degrees of freedom. According to the Timoshenko theory (beam) and the Reissner-Mindlin theory (shell), the formulations account for constant transversal shear strains. To incorporate three dimensional constitutive relations all transversal components of the electric field and the strain field are enriched by mixed finite element interpolations. Thus the complete piezoelectric coupling is appropriately captured. The common assumption of vanishing transversal stress and dielectric displacement components is enforced in an integral sense. Some numerical examples will demonstrate the capability of the presented finite element formulation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Program explanations and causal relevance

Frank Jackson and Philip Pettit have defended a non-reductive account of causal relevance known as the ‘program explanation account’. Allegedly, irreducible mental properties can be causally relevant in virtue of figuring in non-redundant program explanations which convey information not conveyed by explanations in terms of the physical properties that actually do the ‘causal work’. I argue that none of the possible ways to spell out the intuitively plausible idea of a program explanation serves its purpose, viz., defends non-reductive physicalism against Jaegwon Kim’s Causal Exclusion Argument according to which non-reductive physicalism is committed to epiphenomenalism because irreducible mental properties are ‘screened off’ from causal relevance by their physical realizers. Jackson and Pettit’s most promising explication of a program explanation appeals to the idea of invariance of effect under variation of realization, but I show that invariance of effect under variation of realization is neither necessary nor sufficient for causal relevance.