The behaviour of flexible slabs on idealised and actual foundations

Due to a lack of contact between the disciplines of soil mechanics and structural engineering there is a tendency for flexible structures to be analysed under grossly simplified assumptions regarding the interaction between the structure and its soil foundation. For example, it is often assumed that the contact pressure on the base of a structure is uniform, or linearly varying. In the thesis it is proposed that the use of a digital computer enables a structure and its foundation to be analysed as a complete entity. The computer is essential because of the complexity of the mathematical formulation of the problem and because of the scale of the analysis involved. Most of the theoretical work concerns the finite element method for the analysis of structure and foundation, although some work on the finite difference method is also presented. The former method allows a more realistic approximation to be made to the inhomogeneity of soil deposits. An evaluation of current methods and some advances in the theory of the finite element method as applied to plate or slab structures are presented, culminating in an analysis incorporating the effect of transverse shear deformations on the bending of elastic plates. The theories are then applied to the evaluation of a set of experimental results obtained for circular plates bearing on a sand foundation and loaded with concentrated central loads. The classical idealisations of foundations are found to be inadequate and more realistic models are proposed for the particular plate structure and loading case examined

Nonlinear Random Response of Large-Scale Sparse Finite Element Plate Bending Problems

Acoustic fatigue is one of the major design considerations for skin panels exposed to high levels of random pressure at subsonic/supersonic/hypersonic speeds. The nonlinear large deflection random response of the single-bay panels aerospace structures subjected to random excitations at various sound pressure levels (SPLs) is investigated. The nonlinear responses of plate analyses are limited to determine the root-mean-square displacement under uniformly distributed pressure random loads. Efficient computational technologies like sparse storage schemes and parallel computation are proposed and incorporated to solve large-scale, nonlinear large deflection random vibration problems for both types of loading cases: (1) synchronized in time and (2) unsynchronized and statistically uncorrelated in time. For the first time, large scale plate bending problems subjected to unsynchronized load are solved using parallel computing capabilities to account for computational burden due to the simulation of the unsynchronized random pressure fluctuations. The main focus of the research work is placed upon computational issues involved in the nonlinear modal methodologies. A nonlinear FEM method in time domain is incorporated with the Monte Carlo simulation and sparse computational technologies, including the efficient sparse Subspace Eigen-solutions are presented and applied to accurately determine the random response with a refined, large finite element mesh for the first time. Sparse equation solver and sparse matrix operations embedded inside the subspace Eigen-solution algorithms are also exploited. The approach uses the von-Karman nonlinear strain-displacement relations and the classical plate theory. In the proposed methodologies, the solution for a small number (say less than 100) of lowest linear, sparse Eigen-pairs need to be solved for only once, in order to transform nonlinear large displacements from the conventional structural degree-of-freedom (dof) into the modal dof. Moreover, the linear and nonlinear matrices are stored using sparse storage schemes in order to save computational time and memory. In case of unsynchronized load case, the time history needs to be generated and also rescaled separately for each finite element. For problems with large mesh size, the numbers of elements are high and the generation of time histories makes the problem unsolvable (in terms of computational time and/or memory requirements) for all practical purposes. By implementing parallel processing techniques, large scale structural analysis problems are solved without resorting to the use of expensive computing equipment or incurring an inordinately high computational cost that leads to a feasible solution. The reduced and coupled nonlinear equations in modal dof are inexpensively solved by the familiar Runge Kutta numerical integration scheme. Accurate responses are ensured with modal convergence, mesh convergence, and time step studies. The obtained numerical results (for synchronized load case) have also been compared favorably with results obtained from commercialized F.E. code such as Abaqus. Small, medium and large-scale single bay panel models are used to validate and evaluate the numerical performance of the present formulation and its associated computer software

Shape Memory Alloy Applications on Control of Thermal Buckling, Panel Flutter and Random Vibration of Composite Panels

Shape Memory Alloy (SMA) has a unique ability to recover large prestrain (up to 8∼10% elongation for Nitinol, a typical SMA material) completely when the alloy is heated (e.g. aerodynamic heating) above the austenite finish temperature Af. An innovative concept is to utilize the large recovery stress by embedding the prestrained SMA in a traditional fiber-reinforced laminated composite plate, which is called SMA hybrid composite (SMAHC) plate. In this research, static thermal and aerothermal deflections, dynamic panel flutter and random response are investigated for traditional composite plates and SMAHC plates under combined aerodynamic, random and thermal loads by employing nonlinear finite element method. System equations are derived and based on classical laminated plate theory, von Karman nonlinear strain-displacement relation, first-order piston theory aerodynamics and quasi-steady thermal stress theory. Newton-Raphson iterative method is adopted for solving the static thermal and aerothermal buckling deflections. Both normal modes and new proposed aeroelastic modes are employed separately in solution procedures to transform the equations of motion in structural node degree-of-freedom (DOF) into modal equations of motion. Time domain numerical integration technique is adopted for the dynamic analysis under the combined aerodynamic, random and thermal loads. Numerical results of isotropic, traditional composite plates and SMAHC plates are determined, compared and discussed. Various plate behaviors are studied in detail. It is demonstrated that SMAHC plates can greatly suppress or reduce thermal buckling and panel flutter as compared with the traditional composite plates. While the SMAHC plates exhibit better performance at low levels of acoustic excitations, however, the SMAHC plates do not effectively suppress random response at high levels of acoustic excitations

Survey and development of finite elements for nonlinear structural analysis. Volume 1: Handbook for nonlinear finite elements

A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity

FEMs on Composite Meshes for Tuning Plasma Equilibria in Tokamaks

We rely on a combination of different finite element methods on composite meshes, for the simulation of axisymmetric plasma equilibria in tokamaks. One mesh with Cartesian quadrilaterals covers the burning chamber and one mesh with triangles discretizes the region outsidethe chamber. The two meshes overlap in a narrow region around the chamber. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the area that is covered by the plasma, while preserving accurate meshing of the geometric details in the exterior. The continuity of the numerical solution across the boundary of each subdomain is enforced by a mortar-like projection. We show that higher order regularity is very beneficial to improve computational tools for tokamak research.Nous allons utiliser différentes méthodes d’éléments finis sur des maillages composite, pour la simulation des équilibres du plasma dans les tokamaks. Un maillage composé de rectangles avec des quadrilatérales cartésiennes couvre la chambre de combustion et une autre maillage des triangles discrétise la région à l’extérieur de la chambre. Les deux maillages se chevauchent dans une région étroite autour de la chambre. Cette approche a la flexibilité nécessaire pour réaliser facilement et à moindre coût une régularité plus élevé pour l’approximation du flux magnétique dans la zone couverte par le plasma, tout en préservant des détails géométriques à l’extérieur. La continuité de la solution numérique à travers la limite de chaque sous-domaine est imposée par une projection de type mortar. Nous montrons que la régularité d’ordre supérieur est très bénéfique pour affiner les outils de calcul qui sont utilisés en recherche pour mieux maîtriser les experiments dans des tokamaks