The analysis of stiffened plate structures subject to complex loads such as air-blast pressure waves from external or internal explosions, water waves, collisions or simply large static loads is still considered a difficult task. The associated response is highly nonlinear and although it can be solved with currently available commercial finite element programs, the modelling requires many elements with a huge amount of input data and very expensive computer runs. Hence this type of analysis is impractical at the preliminary design stage. The present work is aimed at improving this situation by introducing a new philosophy. That is, a new formulation is developed which is capable of representing the overall response of the complete structure with reasonable accuracy but with a sacrifice in local detailed accuracy. The resulting modelling is relatively simple thereby requiring much reduced data input and run times. It now becomes feasible to carry out design oriented response analyses. Based on the above philosophy, new plate and stiffener beam finite elements are developed for the nonlinear static and dynamic analysis of stiffened plate structures. The elements are specially designed to contain all the basic modes of deformation response which occur in stiffened plates and are called super finite elements since only one plate element per bay or one beam element per span is needed to achieve engineering design level accuracy at minimum cost. Rectangular plate elements are used so that orthogonally stiffened plates can be modelled. The von Karman large deflection theory is used to model the nonlinear geometric behaviour. Material nonlinearities are modelled by von Mises yield criterion and associated flow rule using a bi-linear stress-strain law. The finite element equations are derived using the virtual work principle and the matrix quantities are evaluated by Gauss quadrature. Temporal integration is carried out using the Newmark-β method with Newton-Raphson iteration for the nonlinear equations at each time step. A computer code has been written to implement the theory and this has been applied to the static, vibration and transient analysis of unstiffened plates, beams and plates stiffened in one or two orthogonal directions. Good approximations have been obtained for both linear and nonlinear problems with only one element representations for each plate bay or beam span with significant savings in computing time and costs. The displacement and stress responses obtained from the present analysis compare well with experimental, analytical or other numerical results. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Includes bibliographical references. / This investigation, primarily experimental, examines the failure of circular plates subjected to impulsive velocities. The experiments are conducted on fully clamped circular steel plates subjected to a uniformly distributed impulse. The strain-rate-sensitive mild steel plates fail with mode I (large ductile deformation), mode II (tensile-tearing and deformation) and mode III (transverse-shear) failure modes. The impulse is measured by means of a ballistic pendulum upon which the test plates are attached. During mode II and mode III failure the complete circumferential tearing of the test plate produces a circular disc. The velocity of this disc is recorded. An energy analysis is performed on the test results and an energy balance equation is formulated. Einput = Edeformation + Etearing + Edisc. The input and disc energies are obtained from the experimental measurements and the deformation energy is predicted by using the final deformed height and a shape function together with a rigid-plastic energy analysis adopted by Duffey. Etearing refers to the energy for tensile-tearing in mode II failure or the energy for transverse-shear in mode III failure. Good correlation is found and the experiments show good repeatability. The threshold velocities for the onset of failure modes II and III are given.

Problems which require a study of the static and dynamic response of plates can be approached by first considering the plate to be a portion of an infinite plate, the prescribed boundary conditions being temporarily ignored. Once the plate's boundary has been defined in the infinite plate, a numerical solution is initiated by dividing this boundary into N segments of arbitrary length. For the static case the desired loading can then be applied to the infinite plate, and its effect on the deflection and stresses at the midpoint of the N boundary segments computed. To satisfy the boundary conditions of elementary plate theory, a concentrated force and moment are applied at the midpoint of each boundary segment. The magnitudes of these N equivalent forces and moments are determined by specifying that their combined effects, together with the applied loading, satisfy the boundary conditions at the N boundary points. This yields a set of 2N simultaneous equations whose solution constitutes the solution to the problem. A similar approach can be utilized for the vibrating plate. For the dynamic case the applied loading is assumed as zero, and a harmonically varying force and moment placed at the midpoint of each of the N boundary segments. The magnitudes of the N harmonically varying forces and moments are determined by specifying that their combined effects satisfy the boundary conditions at the N boundary points. This, coupled with the assumption of homogeneous boundary conditions, yields a set of 2N homogeneous equations. The frequency equation follows by setting the determinant of the coefficients equal to zero. The above approach to the solution of boundary value problems is formally known as the Reflection Method. Application of the Reflection Method to the static plate was previously accomplished by placing the equivalent forces and moments in the infinite plate at a finite distance from the midpoint of each boundary segment. This finite distance was called a retracted distance, and the curve along which the equivalent forces and moments were applied, a retracted boundary. In this investigation, the magnitude of the retracted distance was found to influence the condition of the coefficient matrix, while the solution remained relatively independent. The static response of plates by the Reflection Method as presented here applies the equivalent forces and moments directly to the boundary of the plate. This was found to impressively improve the condition of the coefficient matrix and reduce the number of significant figures necessary to obtain a numerical solution. With no increase in the number of boundary points, results were obtained comparable to those utilizing a retracted distance. The equations enabling the forces and moments to be applied directly to the boundary are developed and several examples presented. Application of the Reflection Method to the problem of determining natural frequencies is first illustrated for beams and then extended to plates. In each case the necessary equations are developed and sample problems presented. / Ph. D.

Call number: LD2668 .T4 1966 K78 / Master of Science

published_or_final_version / Mechanical Engineering / Master / Master of Science in Engineering

Finite element formulation based on compatible, assumed displacement fields and the principle of stationary potential energy is applied to analyze edge-stiffened plates. Shear deformation is considered in the formulation of the plate bending and beam bending elements by allowing independent interpolation for displacements and rotations. In addition to bending deformation, plane stress action is superposed on the plate element, while torsion and axial deformation are incorporated in the beam element, so that structural interaction between plate and edge beam elements can be facilitated. By enforcing compatible displacements and rotations across the interface between plate and beam elements, the degrees-of-freedom in one element can be related to the degrees-of-freedom of the adjoining element of a different type. Accordingly, the stiffness matrix and equivalent load vector are transformed to correspond to the common degrees-of-freedom as a result of invariance of the potential energy. By means of the direct stiffness method, the global equilibrium equation is thus established and solved by a frontal solution subroutine. Special features are introduced into the solution subroutine in order to handle varying degrees-of-freedom per node in an element and multiple loading cases. In addition, the speed of input-output transfer between in-core and peripheral storage is optimized. Convergence studies on displacements and stresses show that the current formulation with the program is capable of analyzing shear-flexible structures. The formulation allows convergence of shear-rigid solutions as a limiting case by making use of the selective reduced integration scheme when formulating individual elements. Graphs are presented to aid the design of edge-stiffened plates with two adjacent edges clamped and others cast with intersecting edge beams.

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 68-73).

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

No description available.

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy