Thesis (Engineer)--California Institute of Technology, 1973. / Advisor names found in the Acknowledgments pages of the thesis. Title from home page. Viewed 02/18/2010. Includes bibliographical references.

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In this project, nonlinear behavior of biomembrane are modeled as heterogeneous elastic biological systems. In addition to the static behavior of the membranes, their dynamic behavior are modeled to be able to investigate time-dependency of the variables of the systems. Some of the available models are used and some new ones are developed to study static and dynamic analysis of monolayer and bilayer membranes as well as circular axisymmetric biomembranes. The presented models are developed based on the Euler-Bernoulli constitutive law and employed to investigate buckling phenomena in the membranes as one of the most important physical phenomena in biological environment. Static and dynamic behavior of Buckling phenomenon in biological membranes are modeled. The static model results in nonlinear ordinary di erential equation for one-dimensional approximation. In order to extend the model for circular membranes, the criteria of constant length in one-dimensional membranes is changed to constant surface. Moreover, tension-compression and bending springs are added to the model and employed to study buckling of biomembranes. Similar to the procedure of obtaining the equations of static large deformation of the membrane, the equations of motion of the membrane is obtained using free body diagram of an in finitesimal element of the membrane and employing Euler- Bernoulli constitutive law. Hence, nonlinear integro partial di erential equations are obtained t model the dynamic behavior of the membrane. All of the equations, including static and dynamic ones, are changed to the dimensionless forms so that the results can be considered general and can be employed to analyze diff erent systems with diff erent properties. The nondimensional equations of each part of the project are solved using di erent iterative and time-dependent schemes. The schemes are used to obtain the discretized forms of the equations. The discretized equations of all nodes of the domain, with due attention to the considered boundary conditions, are gathered in a matrix and the matrix solved to obtain the solution of the variables at each node and time stage. The solutions obtained for diff erent problems investigated in this project are employed to illustrate variations of diff erent dependent variables of the models with respect to the independent variables and parameters of the problems. As the important step to analyze the problems, diff erent results of the problems investigated in the project are verifi ed using the available information in literature. Membrane pro le are obtained for di erent parameter values and external forces in the stationary condition. In addition, variation of maximum deflection and slope are studied with respect to the variation of diff erent dimensionless parameters of the system. As a verifi cation of the solution, the incompressibility of bilayer membrane is shown as well. Growth of di fferent variables is shown with respect to time employing the solution of dynamic modeling of the membrane. As one of the important parts of this project, e ects of heterogeneity on dynamic behavior of the membrane under buckling is investigated. The heterogeneous region is considered to have di fferent material properties and it position is changed to also study the geometrical e ffects.

There is a class of plate buckling problems in which buckling occurs in the presence of a constraining medium. This type of buckling has been investigated by many researchers, mainly as buckling of elastic columns and plates on elastic foundations. Analytical solutions have been obtained by assuming the foundation to provide tensile as well as compressive reaction forces. The present work differs from the previous ones in two respects. One, the foundation is assumed to be one-sided, thus providing only the compressive resistance. Two, the plates are allowed to be stressed in the plastic, strain-hardening range. Equations for determining the buckling stresses and wavelengths are obtained by solving the differential equations for simply supported and clamped long rectangular plates stressed uniformly in the longitudinal direction. The relevance and the usefulness of the obtained formulas is demonstrated by comparing the predicted results with the experimental results of other researchers on buckling of concrete filled steel box-section and HSS columns. It is shown that the theoretical buckling loads match quite closely with the experimental ones, and hence, should prove useful in formulating rules for the design of such columns.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1990. / Vita. Abstract. Includes bibliographical references (leaves 69-71). Also available via the Internet.

Thesis (Ph. D.)--Lehigh University, 2004. / Includes vita. Includes bibliographical references (leaves 135-139).

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 169-171).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1966. / Typescript. Vita. Abstracted in Dissertation abstracts, v. 27 (1966) no. 6, p. 1957-B. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

This thesis derives the differential equation for the in plane extentionless buckling of a ring in an elastic foundation. The elastic foundation can exert forces proportional to radial and tangential displacements and a couple proportional to rotation. The external uniform load is always directed toward a fixed point on the initial radius. A special case of this is hydrostatic pressure where the load remains normal to the ring. In other cases the load may remain parallel to the initial radius or remain directed towards the initial centre. Complete solutions are presented for a full ring and several graphs of critical pressure versus foundation stiffness indicating the general behaviour. A full solution is given for a partial ring with hinged supports along with a number of graphs. A method is presented but no solutions are given for a partial ring with fixed supports. Finally, a solution is given for the case of a full ring under hydrostatic load with radial elastic supports having a different spring constant for inward and outward displacements. This solution, presented graphically for all combination of spring constants, can represent the buckling of a culvert under a high fill. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

In this thesis, a stiffness matrix which includes the non-linear effects of principal plane shears, moments and axial loads on lateral and torsional deflections is developed for a doubly symmetric wide flange section. Initially, an exact eight by eight linear matrix is developed for an element of constant section properties. The eight allowable deflections allows the independent representation of the deflections of either flange at either end. The non-linear effects are included in the differential equations by considering the effect of the primary stresses on the equilibrium of a dis-placed element. Two approximations are then introduced. The first consists of a numerical technique for solving the differential equations. The second consists of a simplification of the boundary conditions in solving the differential equations. Using these two approximations, the non-linear portion of the matrix is then built. Several structures are then analyzed. Each structure is divided into several elements. This allows beams of non-constant section properties to be analyzed, and increases the accuracy of the results of the approximate matrices. The results of these analyses are then compared to theoretical results and tabulated. It is seen that the matrix gives good agreement for all cases tested. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate