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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:39:57 +0000Self-similar elastodynamic solutions for the plane wedge
https://resolver.caltech.edu/CaltechETD:etd-11132006-080224
Authors: {'items': [{'id': 'Wojcik-G-L', 'name': {'family': 'Wojcik', 'given': 'Gregory Lynn'}, 'show_email': 'NO'}]}
Year: 1977
DOI: 10.7907/E1D3-0T11
Wave propagation in a two-dimensional elastic wedge is fundamental to a large class of problems in elastodynamic theory, however until now analytical solutions to all but certain degenerate cases were unknown. In this thesis a general elastodynamic solution is derived for the wedge in a state of plane strain. Surface tractions are, restricted to uniform normal and shear loads spreading from the wedge vertex at constant velocity. The geometry and loading then allow self-similar solutions of the governing differential equations and boundary conditions in hyperbolic and elliptic domains. Hyperbolic solutions are found in terms of the elliptic solutions by the method of characteristics, while elliptic solutions are reduced using analytic function theory to two independent Fredholm integral equations of the second kind in one dimension. Although numerical solutions are beyond the scope of the investigation, the integral equations are solvable by standard techniques. Such solutions can be used to solve a number of plane elastodynamic problems involving an edge.https://thesis.library.caltech.edu/id/eprint/4533Failure of Liquid Storage Tanks Due to Earthquake Excitation
https://resolver.caltech.edu/CaltechTHESIS:04132018-090928397
Authors: {'items': [{'id': 'Shih-Choon-Foo', 'name': {'family': 'Shih', 'given': 'Choon-Foo'}, 'show_email': 'NO'}]}
Year: 1981
DOI: 10.7907/m0v8-hs31
<p>Above ground liquid storage tanks have suffered serious damage during earthquakes. The damage of tanks can vary from local yielding or buckling of the tank wall, to loss of contents, or to collapse which leads to an unrepairable tank. Considerable work has been carried out on this problem with varying degree of success. However, the results are largely directed toward response rather than failure prediction. The information on failure mechanisms is very limited. The present work consists of scale model testing, correlation with existing analysis and failure prediction with laboratory verification. The scale model testing incorporates dynamic similarity of the fluid/structure interaction problem. The model study shows that small plastic models can be useful in studying the dynamics and buckling of liquid-filled tanks under ground excitation even though the model does not display complete similitude. The buckling criterion proposed in this study is based upon static considerations and the complex stress field in the shell wall is supplanted by a simple field for which analytical/experimental results are available. Harmonic buckling tests demonstrate that the static buckling criterion is satisfactory even though the prebuckling stress field is time dependent. The harmonic buckling tests, when correlated with the stresses from a response analysis, also indicate that the buckling is largely dependent upon the n = 1 response, Transient buckling tests are also carried out and the results show that the linear analysis together with the static buckling criterion gives a good prediction of the failure of a full fluid-filled tank. The test parameters in these buckling tests include water depth, title angle, thickness of tank wall, top end condition, ground excitation pattern, etc. In addition, buckling tests of unanchored tanks are conducted to study the influence of changing the anchorage of the tank base. An analytical model is suggested to predict the response of an unanchored tank due to overturning moment. The current design criterion of an unĀanchored tank is also assessed in this study. The results of this investigation, in addition to those carried out previously, provide a better understanding of the forced vibration problem, failure criterion and appropriate design procedure for a liquid storage tank.</p>
https://thesis.library.caltech.edu/id/eprint/10805The Analysis of a Nonlinear Difference Equation Occurring in Dynamical Systems
https://resolver.caltech.edu/CaltechETD:etd-07082005-102658
Authors: {'items': [{'email': 'reinhall@u.washington.edu', 'id': 'Reinhall-Per-Gustaf', 'name': {'family': 'Reinhall', 'given': 'Per Gustaf'}, 'show_email': 'YES'}]}
Year: 1982
DOI: 10.7907/X17F-E253
<p>A difference equation with a cubic nonlinearity is examined. Using a phase plane analysis, both quasi-periodic and chaotically behaving solutions are found. The chaotic behavior is investigated in relation to heteroclinic and homoclinic oscillations of stable and unstable solution manifolds emanating from unstable periodic points. Certain criteria are developed which govern the existence of the stochastic behavior. An approximate solution technique is developed giving expressions for the quasi-periodic solutions close to a stable periodic point and the accuracy of these expressions are investigated. The stability of the solutions is examined and approximate local stability criteria are obtained. Stochastic excitation of a nonlinear difference equation is also considered and an approximate value of the second moment of the solution is obtained.</p>https://thesis.library.caltech.edu/id/eprint/2834The Growth of Impact Damage in Compressively Loaded Laminates
https://resolver.caltech.edu/CaltechETD:etd-04132004-084629
Authors: {'items': [{'id': 'Chai-Herzl', 'name': {'family': 'Chai', 'given': 'Herzl'}, 'show_email': 'NO'}]}
Year: 1982
DOI: 10.7907/58D3-ZZ41
<p>The thesis is divided into two chapters. The first chapter describes an experimental program carried out to determine the phenomenological aspects of composite panel failure (graphite/epoxy laminate) under simultaneous in-plane compression and low velocity transverse impact (0-250 ft/sec). High-speed photography and the shadow moire technique were used to record a full-field surface deformation history of the impacted plate. The information gained from these records, supplemented by plate sectioning and observation for interior damage, has shown that the predominant failure mechanism is the coupled effect of delamination and buckling.</p>
<p>In chapter 2, this process of failure is modelled by delamination buckling wherein the local delamination stability, growth or arrest are governed by an energy release rate criterion. Various degrees of problem simplifications are employed, starting with a one-dimensional, delaminated-beam model. In the most sophisticated treatment, it is assumed that the damaged area has an elliptical shape. It was found that this model is capable of describing the growth conditions and the growth behavior of the damaged area. It was also found that the predominant parameter controlling delamination growth or arrest is the fracture energy associated with delamination.</p>
<p>In the appendix at the end of this work, the fracture energy of a composite laminate is considered. A modified cleavage analysis is developed, and is applied to evaluate this quantity for two composite materials of current interest. The test results are then examined with reference to impact damage tolerance data available for these materials. A viscoelastic characterization of the two resins used to fabricate the two composites mentioned above is also provided. The results of these measurements are then examined with reference to long-term applicability of the matrix material.</p>https://thesis.library.caltech.edu/id/eprint/1366Finite Plane and Anti-Plane Elastostatic Fields with Discontinuous Deformation Gradients Near the Tip of a Crack
https://resolver.caltech.edu/CaltechETD:etd-09122006-153033
Authors: {'items': [{'id': 'Fowler-Graeme-Francis', 'name': {'family': 'Fowler', 'given': 'Graeme Francis'}, 'show_email': 'NO'}]}
Year: 1982
DOI: 10.7907/td0f-kr59
<p>In this paper the fully nonlinear theory of finite deformations of an elastic solid is used to study the elastostatic field near the tip of a crack. The special elastic materials considered are such that the differential equations governing the equilibrium fields may lose ellipticity in the presence of sufficiently severe strains.</p>
<p>The first problem considered involves finite anti-plane shear (Mode III) deformations of a cracked incompressible solid. The analysis is based on a direct asymptotic method, in contrast to earlier approaches which have depended on hodograph procedures.</p>
<p>The second problem treated is that of plane strain of a compressible solid containing a crack under tensile (Mode I) loading conditions. The material is characterized by the so-called Blatz-Ko elastic potential. Again, the analysis involves only direct local considerations.</p>
<p>For both the Mode III and Mode I problems, the loss of equilibrium ellipticity results in the appearance of curves ("elastostatic shocks") issuing from the crack-tip across which displacement gradients and stresses are discontinuous.</p>
https://thesis.library.caltech.edu/id/eprint/3502Two Problems in Plane Finite Elastostatics
https://resolver.caltech.edu/CaltechETD:etd-09182006-085128
Authors: {'items': [{'id': 'Connolly-Jeremiah-Finbarr', 'name': {'family': 'Connolly', 'given': 'Jeremiah Finbarr'}, 'show_email': 'NO'}]}
Year: 1983
DOI: 10.7907/yhjy-mb48
<p>In this paper the fully nonlinear equilibrium theory of homogeneous and isotropic incompressible elastic solids is used to study the elastostatic fields in plane strain near the point of application of a concentrated force on a deformed half plane and near the vertex of a circular sector whose plane deformed faces are subjected to prescribed tractions.</p>
<p>In the concentrated force problem, restricting only the form of the elastic potential at large extensional deformations, it is shown that, for materials which "harden" in simple shear, the displacement is bounded at the point of application of the load. This is not the case for materials which "soften" in shear. Estimates of the true stress tensor near the singular point are given.</p>
<p>In the sector problem, for a class of the materials mentioned, the deformation and stress field near the vertex of the deformed cross-section are derived and discussed.</p>
https://thesis.library.caltech.edu/id/eprint/3617Ordinary and Strong Ellipticity in the Equilibrium Theory of Incompressible Hyperelastic Solids
https://resolver.caltech.edu/CaltechETD:etd-11012005-130640
Authors: {'items': [{'id': 'Zee-Layne', 'name': {'family': 'Zee', 'given': 'Layne'}, 'show_email': 'NO'}]}
Year: 1983
DOI: 10.7907/jzka-ce91
<p>In this paper explicit necessary and sufficient conditions are established for the ordinary and strong ellipticity of the three-dimensional field equations in the nonlinear equilibrium theory of incompressible, homogeneous and isotropic, hyperelastic solids. The resulting system of inequalities involves the local principal stretches directly and in addition restricts the first and second partial derivatives of the strain-energy density with respect to the deformation invariants or the principal stretches. The conditions of ordinary and strong ellipticity are found to coalesce for materials that obey the Baker-Ericksen inequalities and possess a positive shear modulus at infinitesimal deformations. Various implications of these ellipticity conditions for special classes of materials and deformations are explored.</p>https://thesis.library.caltech.edu/id/eprint/4358