Sven Klinkel

A continuum based three-dimensional shell element for laminated structures

Abstract In this paper a continuum based three-dimensional shell element for the nonlinear analysis of laminated shell structures is derived. The basis of the present finite element formulation is the standard eight-node brick element with tri-linear shape functions. Especially for thin structures under certain loading cases, the displacement based element is too stiff and tends to lock. Therefore we use assumed natural strain and enhanced assumed strain methods to improve the relatively poor element behaviour. The anisotropic material behaviour of layered shells is modeled using a linear elastic orthotropic material law in each layer. Linear and nonlinear examples show the applicability and effectivity of the element formulation.

Elastic and plastic analysis of thin-walled structures using improved hexahedral elements

In this paper a continuum based 3D–shell element for the nonlinear analysis of thin-walled structures is developed. Assumed natural strain method and enhanced assumed strain method are used to improve the relative poor element behaviour of a standard hexahedral displacement element. Different elastic and inelastic constitutive laws are considered. The anisotropic material behaviour of layered shells is modeled using a hyperelastic orthotropic material law in each layer. Furthermore, finite multiplicative J2-plasticity is discussed. The models are characterized by an interface to the material setting of the boundary value problem. Several examples show the applicability and efficiency of the developed element formulation.

A finite rotation shell theory with application to composite structures

ABSTRACT In this paper we derive a finite element formulation for geometrical nonlinear shell structures. The formulation bases on a direct introduction of the isoparametric finite element formulation into the shell equations. The element allows the occurence of finite rotations which are described by a rotation tensor. A layerwise linear elastic material model for composites is chosen. The consistent linearization of all equations leads to quadratic convergence behaviour within the nonlinear solution procedure. Examples show the applicability and effectivity of the developed element.

Finite Element Formulation of a Piezoelectric Continuum and Performance Studies of Laminar PZT-Patch-Modules

Efficient application of piezoelectric sensors and actuators requires extensive investigations of their loading limits, failure-behavior and life-span under service conditions. Here the performance of laminar PZT-patch-modules is studied, applying a combined approach of experimental and numerical tests. Four-point bending tests are used to evaluate the sensor performance. Linear electro-mechanical coupling is implemented in an 8-node brick user element of the research finite element code FEAP to develop a flexible FE-tool for piezoelectric problems. Comparative FE-analyses of the bending test are carried out in order to assess the capability of the implemented FEAP user element versus the commercially available FE-code ABAQUS. FE-results show good agreement with the experimental tests, different element types yield slight deviations which are discussed.

A geometrically nonlinear mixed finite element formulation for the simulation of piezoelectric shell structures

The paper is concerned with a geometrically nonlinear finite element formulation to analyze piezoelectric shell structures. The classical shell assumptions are extended to the electromechanical coupled problem. The consideration of geometrical nonlinearity includes the analysis of stability problems and other nonlinear effects. The formulation is based on the mixed field functional of Hu-Washizu. The independent fields are displacements, electric potential, strains, electric field, stresses and dielectric displacements. The mixed formulation allows an interpolation of the strains and the electric field through the shell thickness, which is an essential advantage when using nonlinear 3D material laws. With respect to the numerical approximation an arbitrary reference surface of the shell is modeled with a four node element. Each node possesses six mechanical and one electrical degree of freedom. Some simulations demonstrate the applicability of the present piezoelectric shell element.

Advanced Finite Element Formulation for Piezoelectric Smart Shell Structures Under Consideration of Geometrical Nonlinearity

A geometrically nonlinear highly accurate finite element formulation to analyze piezoelectric shell problems is presented. The formulation is based on the mixed field variational principle of Hu-Washizu including the independent fields displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The normal zero stress condition and the normal zero dielectric displacement condition for shells are enforced by the independent resultant stress and resultant dielectric displacement fields. The arbitrary reference surface of the shell is modeled with a four node element. Each node possesses six mechanical degrees of freedom, three displacements and three rotations, and one electrical degree of freedom, which is the difference of the electric potential through the shell thickness. The developed shell element fulfills the patchtests and is able to model arbitrary curved shell structures. Some numerical examples demonstrate the applicability of the present shell element for piezoelectric systems and integrated piezoelectric structures.Copyright