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No description available.

Four different thermoviscoplastic relations, namely, the Litonski-Batra, the Johnson-Cook, the Bodner-Partom and the power law are used to model the thermoviscoplastic response of a material. Each one of these relations accounts for strain hardening, strain-rate hardening and thermal softening of the material. The material parameters in these relations are found by solving an initial-boundary-value problem corresponding to simple shearing deformations so that the computed effective stress vs. the effective plastic strain curves match closely with the experimental data of Marchand and Duffy who tested thin-walled HY-100 steel tubes in torsion. These four viscoplastic relations are used to analyze dynamic thermomechanical deformations of a prenotched plate impacted on the notched side by a cylindrical projectile made of the same material as the plate. The impact loading on the contact surface is simulated by prescribing the time history of the normal component of velocity and null tangential tractions. A plane strain state of deformation is assumed to prevail in the plate and its deformations are studied for different values of the impact speed. The in-house developed finite element code employs constant strain triangular elements, one point integration rule, and a lumped mass matrix. The Lagrangian description of motion is used to describe deformations of the plate. The coupled nonlinear partial differential equations are first reduced to coupled nonlinear ordinary differential equations (ODEs) by using the Galerkin approximation. The ODEs are integrated by using the stiff solver, LSODE, which adaptively adjusts the time step size and computes the solution within the prescribed accuracy. Results computed with the four constitutive relations are found to be qualitatively similar to each other and the general trends agree with the experimental observations in the sense that at low speed of impact, a brittle failure ensues at a point on the upper surface of the notch tip. However, at high impact speeds, a ductile failure in the form of a shear band initiates first from a point on the lower surface of the notch tip. The predicted speed at which the failure mode transitions from brittle to ductile is different for the four viscoplastic relations. Results have been computed using the Bodner-Partom law to study the effects of the notch tip radius and the presence of a circular hole ahead of the notch-tip. For sharp elliptic notch tips, it is found that there is no failure transition speed and the ductile failure always preceeded the brittle failure for the range of the impact speeds studied. For the hole located on the axis of the circular notch tip, the brittle failure always preceeded the ductile failure and it initiated at a point on the lower surface of the circular hole. / Ph. D.

This research presents an analytical investigation of the buckling of eccentrically stiffened orthotropic cylinders and includes the influence of prebuckling deformations. Nonlinear equilibrium equations and boundary conditions are derived by using energy principles. The stiffened cylinder consists of a cylindrical shell made of a homogeneous orthotropic material with eccentric stiffeners on its surface. The rings, or circumferential stiffeners, are considered to be located discretely on circumferential lines along the length of the cylinder and the stringers, or longitudinal stiffeners, are considered to be closely spaced so that their properties can be averaged (smeared out) over the stringer spacing. The stiffeners are considered to be beam elements, to be equally spaced, and to have the stiffener twisting accounted for in an approximate manner. Non-linear Donnell type strain-displacement relations for the shell and the stiffeners are defined and the strain energy of the stiffener-cylinder system is formulated. The governing nonlinear equilibrium equations and boundary conditions are then obtained by the principle of minimum potential energy and the fundamental lemma of calculus of variations. The discrete ring terms are included in the nonlinear equilibrium equations by use of a Dirac delta function. By a perturbation of the nonlinear equilibrium equations and boundary conditions, a set of nonlinear prebuckling equations and boundary conditions and linear buckling equations and boundary conditions are obtained which govern the prebuckling deformations and stresses and buckling of a stiffened orthotropic cylinder with discrete rings. Solutions of the prebuckling and buckling equations are obtained for classical simple support boundary conditions and for loadings of axial compression, lateral pressure, and combinations of axial compression and external or internal pressure. The solutions are obtained by the method of finite differences in which the governing equations and boundary conditions are changed to a system of second order differential equations which are then written in terms of finite differences at stations along the length of the cylinder. The difference equations are formulated in terms of a matrix equation which is solved by a modified G~ussian elimination technique. Solutions of the prebuckling and buckling equations for the case where the rings are considered to be smeared out are presented for comparison with the discrete case. A Galerkin solution of the buckling equations for discrete rings assuming classical prebuckling deformations is also presented in the Appendix. Computed results for two types of contemporary stiffened cylinders are presented in order to study and illustrate the importance of prebuckling deformations, discrete rings, and eccentrically applied compressive loads. The results show that the predicted buckling loads for stiffened cylinders may be substantially affected by using an analysis which takes into account prebuckling deformations. / Doctor of Philosophy

The well-known Timoshenko beam equations (which include transverse shear deformation and rotary inertia effects) are extended for a wide-flanged structure to include the additional shear lag deformation of the flanges; thus, cross-sections of the beam are allowed to distort instead of remaining plane sections. The effect of relative flange bending (bending of the flanges relative to the web) is also included and the integro-differential equations appropriate to the problem are derived. The frequency equation is given in closed form (neglecting the relative flange bending) and solutions for various values of the nondimensional parameters are given. A reduction of the elementary frequency by as much as 40 percent in the first mode is shown. / Master of Science

The steady state of deformation was analyzed for a clayey sand. The use of lubricated end platens was evaluated and proved to reduce the scatter in steady state data. The effect of different data corrections in a steady state analysis was also evaluated. For this investigation the parabolic area assumption better approximated the deformed specimen shape than the right cylinder assumption. It was concluded that the use of different area corrections greatly influences the slope and position of the steady state line. / Master of Science

The Pine Mountain window of Georgia and Alabama hosts the southernmost exposed Grenville aged basement terrane in the Appalachians. The window Is bounded on the east by the Box Ankle thrust fault which juxtaposes basement lithologies from hanging wall paragneiss, schist, and metavolcanic rocks of the Piedmont terrane. The Ocmulgee strike-slip fault separates Piedmont Terrane rocks from Avalon Terrane lithologies to the south and east of the Pine Mountain window. U-Pb ages of zircons constrain the timing of deformation along the Box Ankle and Ocmulgee faults at 304 ± 144 and 335 ± 7 Ma respectively. A contrast in zircon response to high grade deformation from both fault zones is observed. The response of zircon U-Pb systematics in these fault zones provides data on the effects of Pb loss versus U gain models, dissolution processes, and overgrowth binary mixing models from within selected mylonitized bulk rock chemistries. In the Ocmulgee fault, zircon overgrowth associated with deformation dominates U/Pb age discordancy. Isotopic re-equilibration of Sr Isotopes did not occur on a cm whole rock scale during deformation. Porphyroclasts In the Ocmulgee shear zone retained partial Sr Isotopic signatures of the shear zone protolith. In contrast, Rb-Sr Isotope systems In the Box Ankle fault were re-equilibrated during ductile deformation. Zircons from the Box Ankle fault show evidence of dissolution with no apparent overgrowth. A regional tectonic model proposed from ages obtained in this study Include transpression and doming of the basement and Piedmont cover as seen In the Box Ankle fault trace. Dextral strike-slip with right stepover displacement between the Ocmulgee-Goat Rock fault system and the Towaliga system provide a transpressional environment at the eastern end of the Pine Mountain window. / Master of Science

The approach to the problem of a variable thickness plate used in this paper is different from the usual approach in that this paper starts with general stress-strain relations and a generalized form of the position vector as used by Green and Zerna in "Theoretical Elasticity". They use R̅=L[ r̅ (θ₁,θ₂)+ λθ₃a̅₃(θ₁,θ₂)] where θ₁,θ₂, and θ₃ are curvilinear coordinates with θ₁ and θ₂ being the coordinates of the middle surface and λ=t/L being a constant for a plate of constant thickness t. This paper takes λ = λ(θ₁,θ₂) as a function of θ₁ and θ₂ so that the variable thickness may be taken into account. General tensor notation is used so as to work independent of coordinate systems. Making simplifying assumptions only when necessary, the equations of equilibrium and stress-strain relations are derived in terms of tensors connected with the middle surface as was done by Green and Zerna for a constant thickness plate. The additional terms obtained in these equations due to the variation in λ help us to evaluate the effects of the varying thickness. Expressions for stress are developed and they include the effects of transverse shear deformation and normal stress as well as the variation in thickness. These expressions are very much like those used by Essenburg and Naghdi in a paper presented at the Third U.S. National Congress of Applied Mechanics, June, 1958. However, they assumed the form for the stresses while the present paper arrived at their assumed forms with some additional terms after starting with general stress-strain relations. Using the notation of Green and Zerna, a set of nine equations involving the nine unknowns, m ^αβ, w, n^αβ, and v^α is derived and under appropriate boundary conditions, this set will yield a solution to the problem which will be better than the classical solution. Two problems are solved and numerical results are obtained and compared with the classical solutions. One of the problems involves a rectangular plate clamped on one edge with a uniform shear load on the other. The other problem involves a circular ring plate clamped on the outer edge with a uniform shear load on the inner edge. A much better correlation for the deflection of the middle surface is obtained for the rectangular than for the circular ring plate. The deflection at the inner edge of the ring plate obtained by the theory of this paper is over twice that obtained in the classical solution of the same problem. In the previously mentioned set of nine fundamental equations, we have the stress resultants n^αβ and the deflections v^α. With appropriate boundary conditions, these equations could lead to a study of in-plane forces and buckling of variable thickness plates, a field in which not much progress has been made. This paper does not include any numerical work in this direction. It is felt, however, that one of the principal contributions of this paper to the literature is that the set of nine fundamental equations includes the stress resultants in n^αβ thus enabling us to study the effect of in-plane forces as well as that of transverse shear deformation, normal stress, and surface tractions. / Ph. D.

Small-deflection plate equations are presented in terms of the midplane plate deformations and the temperature distribution within the plate, which is assumed independent of the plate deformation. The plate boundary conditions are presented in a general form and are suitable for solutions involving either fixed, free, or hinged edge conditions. The temperature distribution within the plate is assumed to be governed by Poisson's equation and a specified temperature distribution over the surfaces of the plate. Solutions for the temperature distribution are given in terms of a power series with respect to the plate thickness coordinate, the coefficients of which are dependent on the midplane temperature distribution and the midplane temperature gradient in the plate thickness direction. Out-of-plane plate deformations are discussed for plates with fixed edges. Discussions of plate deformations are also presented in which the temperature distributions result from constant heat generation within the plate and from radiation absorption. / Master of Science