A Primary objective of the present research is the development of robust CAE (Computer-Aided Engineering)-based approaches for designing armour plates subjected to ballistic impact by small-calibre hardened peojectiles with or without a protective sheath. Amongst the challenges in simulation is the capturing of target plate material behaviour at high strain rates with possibilities of adiabatic heating. A comprehensive numerical study carried out has resulted in the identification of simulation guidelines using a commercially available explicit finite element anlaysis solver (viz. LS_DYNA). The interferences thus drawn in terms of modeling approach 9I.e. shell, solid or axisymmetric or a mixed representation). Mesh density and element type, contact condition, and constitutive model 9I.e. discrete strain-rate based, Cowper-Symonds, or Johnson-Cook) with failure criteria are verifiable and greatly beneficial for armour plate design. Confidence in the suggested procedures has been obtained through extensive correlation of numerical results with experimental residual velocities and ballistic limits as well as projectile and target plate failure modes. A wide range of impact velocities has been considered (from a low velocity of about 5m/s to an ordnance range velocity of 800+ m/s). Target plates made of variants of mild steel and aluminium alloys have been studied. The simulation approaches have been applied to single-layered as well as multi-layered target plates. Although a majority of the comparisons has been made against published test results, a new ballistic impact testing facility has been set up in course of the current research and excellent correlation of numerically predicted residual velocities and failure modes has been obtained against the tests carried out for aluminium plate using the latter facility. A unique feature of the current experimental effort is the capturing of the complete trajectory of projectile beginning with oblique impact through subsequent perforation/ricochet. Furthermore, projectiles of various nose-shapes such as ogival, conical, hemispherical and blunt have been employed. The power of simulation has been demonstrated with the help of a number of parametric studies with variables such as plate thickness and material properties, as well as projectile mass and diameter, and obtaining physically consistent results. Additionally, existing semi empirical models for residual velocity and ballistic limit prediction have been reviewed, and new user-friendly models have been proposed based on energy conservation and predominant shear plugging failure mode of target plate. Finally, the goal of applying the present research work as a design tool can be well-served by packaging the knowledge gathered here in the form of a user-friendly guide with a graphical user interface(GUI). To this end, an application using MS windows VC++ utilities has been created with the functionalities of: (a) viewing reference LS-DYNA input data files for selecting typical problems of impact on steel and aluminium plates; (b) computing complete lists of strain rate-based material quantities required in LS-DYNA material models like discrete strain rate-based, Cowper-Symonds and Johnson-Cook by specifying the minimum number of easily available quasi-static properties (such as elastic modulus, yield and ultimate strengths, etc.), and (c) estimating residual velocities using the semi-empirical relations for steel and aluminium plates derived in the current work.

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published_or_final_version / Civil Engineering / Master / Master of Philosophy

No description available.

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.

No description available.

The nonlinear static and dynamic response of circular and annular plates under electrostatic, thermal, and combined loading is investigated. The main motivation for the study of these phenomena is providing fundamental insights into the mechanics of micro-electro-mechanical-systems (MEMS). MEMS devices are usually miniaturization of the corresponding macro-scale devices. The basic mechanics of the components of many MEMS devices can be modeled using conventional structural theories. Some of the most used and actively researched MEMS devices- namely pressure sensors and micropumps- use circular or annular diaphragms as principle components. The actuation and sensing principles of these devices are usually electrostatic in nature. Most MEMS devices are required to operate under wide environmental conditions, thus, a study of thermal effects on the performance of these devices is a major design consideration. There exists a wide arsenal of analytic, semi-analytic, and numerical tools for nonlinear analysis of continuous systems. The present work uses different tools for the analysis of different types of problems. The selection of the analysis tools is guided by two principles. The first consideration is that the analysis should reveal the fundamental mechanics and dynamics of the problem rather than simply generating numerical data. The second consideration is numerical efficiency. Guided by the same principles, the basic structural model adopted in this work is the von-Karman plate model. This model captures the basic nonlinear phenomena in the plate with minimal complexity in the equations of motion, thus providing a balance between simplicity and accuracy. We address a wide array of problems for a variety of loading and boundary conditions. We start by analyzing annular plates under static electrostatic loading including the variation of the plate natural frequencies with the applied voltage. We also analyze parametric resonances in plates subjected to sinusoidally varying thermal loads. We investigate the prebuckling and postbuckling static thermal response and the corresponding variation of the natural frequencies. Finally, we close by investigating the problem of a circular plate under a combination of thermal and electrostatic loading. The results of this investigation demonstrate the importance of including nonlinear phenomena in the modeling of MEMS devices both for correct quantitative predictions and for qualitative description of operations. / Ph. D.

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 1958 M39