Geometrically nonlinear analysis of layered composite plates and shells

A degenerated three dimensional finite element, based on the incremental total Lagrangian formulation of a three dimensional layered anisotropic medium was developed. Its use in the geometrically nonlinear, static and dynamic, analysis of layered composite plates and shells is demonstrated. A two dimenisonal finite element based on the Sanders shell theory with the von Karman (nonlinear) strains was developed. It is shown that the deflections obtained by the 2D shell element deviate from those obtained by the more accurate 3D element for deep shells. The 3D degenerated element can be used to model general shells that are not necessarily doubly curved. The 3D degenerated element is computationally more demanding than the 2D shell theory element for a given problem. It is found that the 3D element is an efficient element for the analysis of layered composite plates and shells undergoing large displacements and transient motion

Single side damage simulations and detection in beam-like structures

Beam-like structures are the most common components in real engineering, while single side damage is often encountered. In this study, a numerical analysis of single side damage in a free-free beam is analysed with three different finite element models; namely solid, shell and beam models for demonstrating their performance in simulating real structures. Similar to experiment, damage is introduced into one side of the beam, and natural frequencies are extracted from the simulations and compared with experimental and analytical results. Mode shapes are also analysed with modal assurance criterion. The results from simulations reveal a good performance of the three models in extracting natural frequencies, and solid model performs better than shell while shell model performs better than beam model under intact state. For damaged states, the natural frequencies captured from solid model show more sensitivity to damage severity than shell model and shell model performs similar to the beam model in distinguishing damage. The main contribution of this paper is to perform a comparison between three finite element models and experimental data as well as analytical solutions. The finite element results show a relatively well performanc

A finite element modelling methodology for the non-linear stiffness evaluation of adhesively bonded single lap-joints. Part 2, Novel shell mesh to minimise analysis time

A new modelling methodology is presented that enables the stiffness of adhesively bonded single lap-joints to be included in the finite element analysis of whole vehicle bodies. This work was driven by the need to significantly reduce computing resources for vehicle analysis. To achieve this goal the adhesive bond line and adherends are modelled by a relatively ‘small’ number of shell elements to replace the usual solid element mesh for a reliable analysis. Previous work in Part 1 has provided the necessary background information to develop and verify the new finite element analysis that reduces the solution runtime by a factor of 1000. Although a joint’s non-linear stiffness is reliably simulated to failure load, it is recognised by the authors that the coarse shell mesh cannot provide accurate peak stresses or peak strains for the successful application of a numerical failure criterion. Given that the new modelling methodology is very quick to apply to existing shell models of vehicle bodies, it is recommended for use by the stress analyst who requires, say at the preliminary design stage, whole vehicle stiffness performance in a significantly reduced timeframe

Limit-point buckling analyses using solid, shell and solid–shell elements

In this paper, the recently-developed solid-shell element SHB8PS is used for the analysis of a representative set of popular limit-point buckling benchmark problems. For this purpose, the element has been implemented in Abaqus/Standard finite element software and the modified Riks method was employed as an efficient path-following strategy. For the. benchmark problems tested, the new element shows better performance compared to solid elements and often performs as well as state-of-the-art shell elements. In contrast to shell elements, it allows for the accurate prescription of boundary conditions as applied to the actual edges of the structure.Agence Nationale de la Recherche, France (ANR-005-RNMP-007

Isogeometric FEM-BEM coupled structural-acoustic analysis of shells using subdivision surfaces

We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The Kirchhoff-Love shell equation is discretised with the finite element method and the Helmholtz equation for the acoustic field with the boundary element method. The use of the boundary element formulation allows the elegant handling of infinite domains and precludes the need for volumetric meshing. In the present work the subdivision control meshes for the shell displacements and the acoustic pressures have the same resolution. The corresponding smooth subdivision basis functions have the $C^1$ continuity property required for the Kirchhoff-Love formulation and are highly efficient for the acoustic field computations. We validate the proposed isogeometric formulation through a closed-form solution of acoustic scattering over a thin shell sphere. Furthermore, we demonstrate the ability of the proposed approach to handle complex geometries with arbitrary topology that provides an integrated isogeometric design and analysis workflow for coupled structural-acoustic analysis of shells

Analysis of axisymmetric laminated composite shells subjected to asymmetric loading

A finite element formulation for the static analysis of a laminated composite shell of revolution with general meridional curvature, subjected to asymmetric loading, is presented. The analysis uses an axisymmetric laminated shell element where the shell geometry is satisfactorily represented; higher order polynomial approximations are used for the displacement fields. The asymmetric loading problem is handled through a Fourier series representation of the applied loads and the resultant displacements. Solutions are presented for typical aerospace shell structures like a composite cone and a tangent ogive shell subjected to wind loads

Optimum design of a gearbox for low vibration

A computer program was developed for designing a low vibration gearbox. The code is based on a finite element shell analysis, a modal analysis, and a structural optimization method. In the finite element analysis, a triangular shell element with 18 degrees-of-freedom is used. In the optimization method, the overall vibration energy of the gearbox is used as the objective function and is minimized at the exciting frequency by varying the finite element thickness. Modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variable. The sensitivity is representative of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. The computer code is applied to a design problem derived from an experimental gearbox in use at the NASA Lewis Research Center. The top plate and two side plates of the gearbox are redesigned and the contribution of each surface to the total vibration is determined. Results show that optimization of the top plate alone is effective in reducing total gearbox vibration