Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability

On rotational instability within the nonlinear six-parameter shell theory

Within the six-parameter nonlinear shell theory we analyzed the in-plane rotational instability which occurs under in-plane tensile loading. For plane deformations the considered shell model coincides up to notations with the geometrically nonlinear Cosserat continuum under plane stress conditions. So we considered here both large translations and rotations. The constitutive relations contain some additional micropolar parameters with so-called coupling factor that relates Cosserat shear modulus with the Cauchy shear modulus. The discussed instability relates to the bifurcation from the static solution without rotations to solution with non-zero rotations. So we call it rotational instability. We present an elementary discrete model which captures the rotational instability phenomenon and the results of numerical analysis within the shell model. The dependence of the bifurcation condition on the micropolar material parameters is discussed

Strategien zur Loesung nichtlinearer Probleme der Strukturmechanik und ihre modulare Aufbereitung im Konzept MESY

TIB: RN 4503 (48)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Finite elements for irregular nonlinear shells

Starting with a short overview of the basic concepts in the finite element analysis of shells, a summary of the complete set of shell governing equations is given together with the formulation of the momentum balance law in a weak form (principle of virtual displacements). On this basis a general iterative procedure is described which is needed in the solution of nonlinear shell problems, and the corresponding variational principles with relaxed regularity requirements are formulated. These principles provide the mathematical basis for the formulation of different classes of shell finite elements. Finally, the numerical analysis of linearly elastic shells is presented. The numerical results cover a large menu of illustrative test examples of complex plate and doubly curved shell structures, for which linear and nonlinear solutions with a pre- and post-buckling analysis are discussed. (WEN)Available from TIB Hannover: RN 4503(96) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman