A thick anisotropic plate element in the framework of an absolute nodal coordinate formulation
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O R I G I N A L PA P E R
A thick anisotropic plate element in the framework of an absolute nodal coordinate formulation M. Langerholc · J. Slaviˇc · M. Boltežar
Received: 28 June 2012 / Accepted: 15 January 2013 / Published online: 26 January 2013 © Springer Science+Business Media Dordrecht 2013
Abstract In this research, the incorporation of material anisotropy is proposed for the large-deformation analyses of highly flexible dynamical systems. The anisotropic effects are studied in terms of a generalized elastic forces (GEFs) derivation for a continuumbased, thick, and fully parameterized absolute nodal coordinate formulation plate element, of which the membrane and bending deformation effects are coupled. The GEFs are first derived for a fully anisotropic, linearly elastic material, characterized by 21 independent material parameters. Using the same approach, the GEFs are obtained for an orthotropic material, characterized by nine material parameters. Furthermore, the analysis is extended to the case of nonlinear elasticity; the GEFs are introduced for a nonlinear Cauchy-elastic material, characterized by four inplane orthotropic material parameters. Numerical simulations are performed to validate the theory for statics and dynamics and to observe the anisotropic responses in terms of displacements, stresses, and strains. The presented formulations are suitable for studying the nonlinear dynamical behavior of advanced elastic materials of an arbitrary degree of anisotropy.
M. Langerholc Knauf Insulation d.o.o., Central Engineering Europe, Trata 32, 4220 Škofja Loka, Slovenia M. Langerholc · J. Slaviˇc · M. Boltežar () Faculty of mechanical engineering, Aškerˇceva 6, 1000 Ljubljana, Slovenia e-mail: [email protected]
Keywords Absolute nodal coordinate formulation · Thick plate · Anisotropy · Nonlinear elasticity · Nonlinear dynamics · Large deformation
1 Introduction Analyzing the nonlinear dynamical behavior of complex engineering processes is becoming increasingly important, as the consideration of large deformations, the implementation of active external loadings, damping, friction or contact effects, together with advanced, nonlinear, constitutive laws, and material anisotropy, have in the past two decades put an emphasis on research in this field. Special large-deformation formulations were proposed to address the problems of nonlinear dynamics that allow the implementation of both the geometrical and material nonlinearities. Among the most recently proposed formulations is the absolute nodal coordinate formulation (ANCF). The ANCF has been implemented in many different areas of mechanics, such as characterization of highly nonlinear dynamical systems [2, 9, 27, 29], studying contact problems [6, 7, 11], or even the field of the digital image correlation [15]. Established especially to deal with highly flexible structures, the main features of the ANCF are a constant mass matrix, zero centrifugal and Coriolis inertia forces, and the possibility of exact rigid-body movement modeling. Since the A
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