Recent advances in nonlinear passive vibration isolators

Since the mid-1960s when the forms of curved shell finite elements were originated, including those pioneered by Professor Gallagher, the published literature on the subject has grown extensively. The first two present authors and Liaw presented a survey of such literature in 1990 in this journal. Professor Gallagher maintained an active interest in this subject during his entire academic career, publishing milestone research works and providing periodic reviews of the literature. In this paper, we endeavor to summarize the important literature on shell finite elements over the past 15 years. It is hoped that this will be a befitting tribute to the pioneering achievements and sustained legacy of our beloved Professor Gallagher in the area of shell finite elements. This survey includes: the degenerated shell approach; stress-resultant-based formulations and Cosserat surface approach; reduced integration with stabilization; incompatible modes approach; enhanced strain formulations; 3-D elasticity elements; drilling d.o.f. elements; co-rotational approach; and higher-order theories for composites. Copyright © 2000 John Wiley & Sons, Ltd.

A survey of recent shell finite elements

This paper presents a state of the art review on geometrically nonlinear analysis of shell structures that is limited to the co-rotational approach and to flat triangular shell finite elements. These shell elements are built up from flat triangular membranes and plates. We propose an element comprised of the constant strain triangle (CST) membrane element and the discrete Kirchhoff (DKT) plate element and describe its formulation while stressing two main issues: the derivation of the geometric stiffness matrix and the isolation of the rigid body motion from the total deformations. We further use it to solve a broad class of problems from the literature to validate its use.

Geometrically Nonlinear Analysis of Shell Structures Using a Flat Triangular Shell Finite Element

Flexible flapping wings have garnered a large amount of attention within the micro aerial vehicle (MAV) community: a critical component of MAV flight is the coupling of aerodynamics and structural dynamics. This paper presents a computational framework for simulating shell-like wing structures flapping in incompressible flow at low Reynolds numbers in both hover and forward flight. The framework is developed by coupling an in-house co-rotational finite element structural dynamics solver suitable for small strain and large rotations, to an in-house pressure-based Navier-Stokes solver. The development of the computational structural dynamics (CSD) solver and its coupling with the computational fluid dynamics (CFD) solver is discussed in detail. Validation studies are presented for both the CSD and the aeroelastic solvers using different wing configurations. Structural dynamics solutions are presented for rectangular wings with either a prescribed plunge or a single degree-of-freedom flapping motion. The aeroelastic response is computed for two different wing configurations: 1) a thin-plate rectangular aluminum wing (aspect ratio 6) undergoing a single-axis large amplitude flapping motion and 2) a rectangular wing of NACA0012 cross-section (aspect ratio 6) under a pure plunge motion. Results are validated against available experimental data and those obtained from a different aeroelasticity framework previously developed by the authors.

/pdf/flapping-wing-cfd-csd-aeroelastic-formulation-based-on-a-co-srdgotjjop.pdf

Flapping Wing CFD/CSD Aeroelastic Formulation Based on a Co- rotational Shell Finite Element

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Finite element linear and nonlinear, static and dynamic analysis of structural elements: a bibliography (1992‐1995)

A co-rotational, updated Lagrangian formulation for geometrically nonlinear finite element analysis of shell structures

Numerical characterisation of nonlinear stiffness properties of pre-stressed vibration isolation mounts was presented. A computational procedure was developed to evaluate the condensed stiffness matrix of vibration isolators required by the vibration of viscoelastic and elastic structures (VVES) program. The procedure was based on a nonlinear finite element program which is able to handle complicated mount geometry and nonlinear effect associated with the static pre-loading. Three practical vibration isolation mount structures were analyzed and satisfactory numerical results were obtained.

/pdf/numerical-characterisation-of-nonlinear-stiffness-properties-4bydz5o8f0.pdf

Michael W. Chernuka

Papers

A co-rotational, updated Lagrangian formulation for geometrically nonlinear finite element analysis of shell structures

Numerical characterisation of nonlinear stiffness properties of pre-stressed vibration isolation mounts