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

Galerkin projection of discrete fields via supermesh construction

Interpolation of discrete FIelds arises frequently in computational physics. This thesis focuses on the novel implementation and analysis of Galerkin projection, an interpolation technique with three principal advantages over its competitors: it is optimally accurate in the L2 norm, it is conservative, and it is well-defined in the case of spaces of discontinuous functions. While these desirable properties have been known for some time, the implementation of Galerkin projection is challenging; this thesis reports the first successful general implementation. A thorough review of the history, development and current frontiers of adaptive remeshing is given. Adaptive remeshing is the primary motivation for the development of Galerkin projection, as its use necessitates the interpolation of discrete fields. The Galerkin projection is discussed and the geometric concept necessary for its implementation, the supermesh, is introduced. The efficient local construction of the supermesh of two meshes by the intersection of the elements of the input meshes is then described. Next, the element-element association problem of identifying which elements from the input meshes intersect is analysed. With efficient algorithms for its construction in hand, applications of supermeshing other than Galerkin projections are discussed, focusing on the computation of diagnostics of simulations which employ adaptive remeshing. Examples demonstrating the effectiveness and efficiency of the presented algorithms are given throughout. The thesis closes with some conclusions and possibilities for future work

C0 triangular elements based on the Refined Zigzag Theory for multilayered composite and sandwich plates

The Refined Zigzag Theory (RZT) has been recently developed for the analysis of homogeneous, multilayer composite and sandwich plates. The theory has a number of practical and theoretical advantages over the widely used First-order Shear Deformation Theory (FSDT) and other types of higher-order and zigzag theories. Using FSDT as a baseline, RZT takes into account the stretching, bending, and transverse shear deformations. Unlike FSDT, this novel theory does not require shear correction factors to yield accurate results for a wide range of material systems including homogeneous, laminated composite, and sandwich laminates. The inplane zigzag kinematic assumptions, which compared to FSDT add two additional rotation-type kinematic variables, give rise to two types of transverse shear strain measures - the classical average shear strain (as in FSDT) and another one related to the cross-sectional distortions enabled by the zigzag kinematic terms. Consequently, with a fixed number of kinematic variables, the theory enables a highly accurate modeling of multilayer composite and sandwich plates even when the laminate stacking sequence exhibits a high degree of transverse heterogeneity. Unlike most zigzag formulations, this theory is not affected by such theoretical anomalies as the vanishing of transverse shear stresses and forces along clamped boundaries. In this paper, six- and three-node, C0-continuous, RZT-based triangular plate finite elements are developed; they provide the best compromise between computational efficiency and accuracy. The element shape functions are based on anisoparametric (aka interdependent) interpolations that ensure proper element behavior even when very thin plates are modeled. Continuous edge constraints are imposed on the transverse shear strain measures to derive coupled-field deflection shape functions, resulting in a simple and efficient three-node element. The elements are implemented in ABAQUS - a widely used commercial finite element code - by way of a user-element subroutine. The predictive capabilities of the new elements are assessed on several elasto-static problems, which include simply supported and cantilevered laminated composite and sandwich plates. The numerical results demonstrate that the new RZT-based elements provide superior predictions for modeling a wide range of laminates including highly heterogeneous sandwich laminations. They also offer substantial improvements over the existing plate elements based on FSDT as well as other higher-order and zigzag-type element

A Comparison of Numerical Methods used for\ud Finite Element Modelling of Soft Tissue\ud Deformation

Soft tissue deformation is often modelled using incompressible nonlinear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular, the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. We investigate the effect of these choices on the accuracy of the computed solution, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. We set up model problems with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). We find that the choice of pressure basis functions are vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general that it is important to take the expected regularity of the solution into account when choosing a numerical scheme

Patient-specific anisotropic model of human trunk based on MR data

There are many ways to generate geometrical models for numerical simulation, and most of them start with a segmentation step to extract the boundaries of the regions of interest. This paper presents an algorithm to generate a patient-specific three-dimensional geometric model, based on a tetrahedral mesh, without an initial extraction of contours from the volumetric data. Using the information directly available in the data, such as gray levels, we built a metric to drive a mesh adaptation process. The metric is used to specify the size and orientation of the tetrahedral elements everywhere in the mesh. Our method, which produces anisotropic meshes, gives good results with synthetic and real MRI data. The resulting model quality has been evaluated qualitatively and quantitatively by comparing it with an analytical solution and with a segmentation made by an expert. Results show that our method gives, in 90% of the cases, as good or better meshes as a similar isotropic method, based on the accuracy of the volume reconstruction for a given mesh size. Moreover, a comparison of the Hausdorff distances between adapted meshes of both methods and ground-truth volumes shows that our method decreases reconstruction errors faster. Copyright © 2015 John Wiley & Sons, Ltd.Natural Sciences and Engineering Research Council (NSERC) of Canada and the MEDITIS training program (´Ecole Polytechnique de Montreal and NSERC)

Development and Monte Carlo validation of a finite element reactor analysis framework

This study presents the development and Monte Carlo validation of a continuous Galerkin finite element reactor analysis framework. In its current state, the framework acts as an interface between the mesh preparation software GMSH and the sparse linear solvers in MATLAB, for the discretization and approximation of 1-D, 2-D, and 3-D linear partial differential equations. Validity of the framework is assessed from the following two benchmarking activities: the 2-D IAEA PWR benchmark; and the 2-D Missouri Science and Technology Reactor benchmark proposed within this study. The 2-D IAEA PWR multi-group diffusion benchmark is conducted with the following discretization schemes: linear, quadratic, and cubic triangular elements; linear and quadratic rectangular elements of mesh sizes 10, 5, 2, 1, 0.5 cm. Convergence to the reference criticality eigenvalue of 1.02985 is observed for all cases. The proposed 2-D MSTR benchmark is prepared through translation of an experimentally validated 120w core configuration MCNP model into Serpent 2. Validation of the Serpent 2 model is attained from the comparison of criticality eigenvalues, flux traverses, and two 70-group energy spectrums within fuel elements D5 and D9. Then, a two-group 2-D MSTR benchmark of the 120w core configuration is prepared with the spatial homogenization methodology implemented within Serpent 2. Final validation of the framework is assessed from the comparison of criticality eigenvalues and spatial flux solutions of the diffusion and simplified spherical harmonics SP3 models. The diffusion model resulted in a difference in reactivity of Δρ =-1673.93 pcm and the SP3 model resulted in a difference of Δρ = -777.60 pcm with respect to the Serpent 2 criticality eigenvalues --Abstract, page iii