Orthotropic rotation-free thin shell elements

A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction for all elements. This transformation is carried out solely in the undeformed state leaving minimal additional impact on the computational effort expended to simulate orthotropic materials compared to isotropic, resulting in a straightforward and highly efficient implementation. This method is implemented for rotation-free triangular shells using the finite element framework built on the Kirchhoff--Love theory employing subdivision surfaces. The accuracy of this approach is demonstrated using the deformation of a pinched hemispherical shell (with a 18{\deg} hole) standard benchmark. To showcase the efficiency of this implementation, the wrinkling of orthotropic sheets under shear displacement is analyzed. It is found that orthotropic subdivision shells are able to capture the wrinkling behavior of sheets accurately for coarse meshes without the use of an additional wrinkling model.Comment: 10 pages, 8 figure

Influence of boundary conditions and geometric imperfections on lateral–torsional buckling resistance of a pultruded FRP I-beam by FEA

Presented are results from geometric non-linear finite element analyses to examine the lateral torsional buckling (LTB) resistance of a Pultruded fibre reinforced polymer (FRP) I-beam when initial geometric imperfections associated with the LTB mode shape are introduced. A data reduction method is proposed to define the limiting buckling load and the method is used to present strength results for a range of beam slendernesses and geometric imperfections. Prior to reporting on these non-linear analyses, Eigenvalue FE analyses are used to establish the influence on resistance of changing load height or displacement boundary conditions. By comparing predictions for the beam with either FRP or steel elastic constants it is found that the former has a relatively larger effect on buckling strength with changes in load height and end warping fixity. The developed finite element modelling methodology will enable parametric studies to be performed for the development of closed form formulae that will be reliable for the design of FRP beams against LTB failure

Orthotropic rotation-free basic thin shell triangle

A methodology for the geometrically nonlinear analysis of orthotropic shells using a rotation-free shell triangular element is developed. The method is based on the computation of the strain and stress fields in the principal fiber orientation of the material. Details of the definition of the fiber orientation in a mesh of triangles and of the general formulation of the orthotropic rotation-free element are given. The accuracy of the formulation is demonstrated in examples of application

Shear-flexible finite-element models of laminated composite plates and shells

Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters

A finite element for thermal stress analysis of shells of revolution

A new finite element is described for performing detailed thermal stress analysis of thin orthotropic shells of revolution. The element provides for temperature loadings which may vary over the surface of the shell as well as through the thickness. In a number of sample calculations, results from the present method are compared with analytical solutions as well as with independent numerical analyses. Such calculations are carried out for two cylinders, a conical frustum, a truncated hemisphere, and an annular plate. Generally, the agreement between the present solution and the other solutions is excellent

Numerical nonlinear inelastic analysis of stiffened shells of revolution. Volume 1: Theory manual for STARS-2P digital computer program

The theoretical analysis background for the STARS-2P nonlinear inelastic program is discussed. The theory involved is amenable for the analysis of large deflection inelastic behavior in axisymmetric shells of revolution subjected to axisymmetric loadings. The analysis is capable of considering such effects as those involved in nonproportional and cyclic loading conditions. The following are also discussed: orthotropic nonlinear kinematic hardening theory; shell wall cross sections and discrete ring stiffeners; the coupled axisymmetric large deflection elasto-plastic torsion problem; and the provision for the inelastic treatment of smeared stiffeners, isogrid, and waffle wall constructions

Rational placement of a macro fibre composite actuator in composite rotating beams

In the presented research the dynamics of a thin rotating composite beam with surface bonded MFC actuator are considered. A parametric analysis aimed at finding the most efficient location of the actuator on the beam is presented. Gyroscopic effects resulting in the beam’s initial strain and therefore non-zero voltage in PZT are taken into account. Within the frame of the study maximising the system's response observed in vibration modes for uncoupled and coupled motions is examined. The results are compared to the case of a nonrotating beam and also to the maximum response of the beam with the actuator placed at different positions. To perform the analysis an ABAQUS finite element model of an electromechanical system under consideration is developed. The multi-layer composite beam structure is modelled by shell elements according to a layup-ply technique; the MFC actuator is modelled by 3D coupled field piezoelectric elements. Both modal analysis and frequency response spectra are performed to obtain the structural modal parameters and response amplitude, respectively. The analysis is repeated for three different orientations of the beam's cross-section with respect to the plane of rotation (i.e. arbitrary assumed pitch angles); in all cases the condition constant angular speed is preserved. This work is fundamental for continuing the research for control of dynamics of rotating composite beams with active elements

Wrinkling and folding analysis of elastic membranes using an enhanced rotation-free thin shell triangular element

This paper presents a formulation for analysis of thin elastic membranes using a rotation-free shell element within an explicit time integration strategy. The applications presented are isotropic/anisotropic rectangular membranes under shear forces and fabric drapes falling over a pedestal. Results are compared with other numerical results existing in the literature

Multiparameter actuation of a neutrally-stable shell: a flexible gear-less motor

We have designed and tested experimentally a morphing structure consisting of a neutrally stable thin cylindrical shell driven by a multiparameter piezoelectric actuation. The shell is obtained by plastically deforming an initially flat copper disk, so as to induce large isotropic and almost uniform inelastic curvatures. Following the plastic deformation, in a perfectly isotropic system, the shell is theoretically neutrally stable, owning a continuous manifold of stable cylindrical shapes corresponding to the rotation of the axis of maximal curvature. Small imperfections render the actual structure bistable, giving preferred orientations. A three-parameter piezoelectric actuation, exerted through micro-fiber-composite actuators, allows us to add a small perturbation to the plastic inelastic curvature and to control the direction of maximal curvature. This actuation law is designed through a geometrical analogy based on a fully non-linear inextensible uniform-curvature shell model. We report on the fabrication, identification, and experimental testing of a prototype and demonstrate the effectiveness of the piezoelectric actuators in controlling its shape. The resulting motion is an apparent rotation of the shell, controlled by the voltages as in a "gear-less motor", which is, in reality, a precession of the axis of principal curvature.Comment: 20 pages, 9 figure