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Mechanical & Aerospace Engineering Theses & Dissertations

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Electron Beam Irradiation Effects On Bulk Metals And High Entropy Alloys (Crmnv And Crmntiv) And The Synthesis And Characterization Of Irradiation-Induced Damage In Polycrystalline Metal And High Entropy Alloy Thin Films, Najmin Ara Sultana Jul 2025

Electron Beam Irradiation Effects On Bulk Metals And High Entropy Alloys (Crmnv And Crmntiv) And The Synthesis And Characterization Of Irradiation-Induced Damage In Polycrystalline Metal And High Entropy Alloy Thin Films, Najmin Ara Sultana

Mechanical & Aerospace Engineering Theses & Dissertations

Accelerator beam exit windows are designed to withstand intense radiation and mechanical stress while preserving beam transmission and structural integrity. This dissertation explores the structural and mechanical responses of pure metals and high-entropy alloys (HEAs), in both bulk and thin-film forms, under high-dose electron beam (e-beam) irradiation to identify optimal materials for next-generation accelerator exit windows. Monte Carlo simulations using FLUKA, conducted at Jefferson Lab, revealed that amongst Ni, Ti, Cr, and V, Ni exhibits the highest power dissipation, while Ti depicts the lowest power dissipation, with Cr and V demonstrating intermediate characteristics. Bulk polycrystalline (PC) and single-crystalline (SC) samples …


Intrinsic Manipulation Of Microstructure And Strength Of Ice-Templated Lithium Titanate, Rohan Parai Oct 2024

Intrinsic Manipulation Of Microstructure And Strength Of Ice-Templated Lithium Titanate, Rohan Parai

Mechanical & Aerospace Engineering Theses & Dissertations

This dissertation focuses on developing a fabrication landscape first time ever for directionally porous lithium titanate (LTO) materials using ice-templating technique. Ice-templating, a promising fabrication technique for porous ceramics, enables the formation of sintered structures with anisotropic pores that are aligned to improve mechanical stability of materials.

The work presented in this dissertation addresses advancements in tuning the porosity, strength, and microstructural characteristics of ice-templated LTO materials through adjustments of intrinsic variables, including sucrose as a water-soluble additive, variations in freezing front velocity, solute concentration, and solid loading. First, this study demonstrated that adding sucrose in LTO suspensions increased the …


Switching Methods For Three-Dimensional Rotational Dynamics Using Modified Rodrigues Parameters, Matthew Jarrett Banks Oct 2023

Switching Methods For Three-Dimensional Rotational Dynamics Using Modified Rodrigues Parameters, Matthew Jarrett Banks

Mechanical & Aerospace Engineering Theses & Dissertations

A rigid body in space has three degrees of rotational freedom. As a result, a minimum of three independent parameters is required to define the three-dimensional orientation of a rigid body. As is well known, every set of three independent parameters has at least one orientation where mathematical or geometrical singularities are encountered; therefore, when the use of a three-parameter representation is desired, a method for singularity avoidance must also be considered. A common practice for singularity avoidance is to switch between parameter sets whose singularities occur at different orientations. With this in mind, modified Rodrigues parameters (MRP) are considered …


Development, Experimental Validation, And Progressive Failure Modeling Of An Ultra-Thin High Stiffness Deployable Composite Boom For In-Space Applications, Jimesh D. Bhagatji Aug 2023

Development, Experimental Validation, And Progressive Failure Modeling Of An Ultra-Thin High Stiffness Deployable Composite Boom For In-Space Applications, Jimesh D. Bhagatji

Mechanical & Aerospace Engineering Theses & Dissertations

To maximize the capabilities of nano- and micro-class satellites, which are limited by their size, weight, and power, advancements in deployable mechanisms with a high deployable surface area to packaging volume ratio are necessary. Without progress in understanding the mechanics of high-strain materials and structures, the development of compact deployable mechanisms for this class of satellites would be difficult. This research focuses on fabrication, experimental testing, and progressive failure modelling to study the deformation of an ultra-thin composite beam. The research study examines deformation modes of a boom under repetitive pure bending loads using 4-point bending setup. The material and …


Indentation Creep Analysis For Self Similar Indenters, Sandeep V. Thube Oct 2009

Indentation Creep Analysis For Self Similar Indenters, Sandeep V. Thube

Mechanical & Aerospace Engineering Theses & Dissertations

In indentation creep experiments, it is difficult to characterize the mechanical properties of small size specimens using conventional methods. This study uses finite element modeling to investigate rate-sensitive deformation of materials with different hardness and strain rate sensitivities for self similar indenter tip geometries. The simulation model is developed using commercially available finite element software Abaqus/Standard. Our study investigates the difference between strain rate sensitivity of hardness (vH) and of flow stress (vu) and their relation to the hardness/modulus ratio. It reveals that the commonly held assumption that vH = vu is violated except for materials with low hardness/modulus …


Hypersonic Boundary Layer Receptivity To Acoustic Disturbances Over Cones, Kursat Kara Jan 2008

Hypersonic Boundary Layer Receptivity To Acoustic Disturbances Over Cones, Kursat Kara

Mechanical & Aerospace Engineering Theses & Dissertations

The receptivity mechanisms of hypersonic boundary layers to free stream acoustic disturbances are studied using both linear stability theory (LST) and direct numerical simulations (DNS). A computational code is developed for numerical simulation of steady and unsteady hypersonic flow over cones by combining a fifth-order weighted essentially non-oscillatory (WENO) scheme with third-order total-variation-diminishing (TVD) Runge-Kutta method. Hypersonic boundary layer receptivity to free-stream acoustic disturbances in slow and fast modes over 5-degree, half-angle blunt cones and wedges are numerically investigated. The free-stream Mach number is 6.0, and the unit Reynolds number is 7.8×106/ft. Both the steady and unsteady solutions are obtained …


Statistical Interpretation Of Mohr-Coulomb Theory As Applied To Fracture In Brittle Materials Containing Cracks, Mudit J. Monsi Jul 2006

Statistical Interpretation Of Mohr-Coulomb Theory As Applied To Fracture In Brittle Materials Containing Cracks, Mudit J. Monsi

Mechanical & Aerospace Engineering Theses & Dissertations

Fracture in brittle materials containing pre-existing cracks was studied. The probability of of crack growth under both shear and tensile stresses was determined for an arbitrary distribution of crack sizes. Two different crack orientation distributions, random and uniform, as well as friction were also taken into account. The material's reliability was assumed to depend on the number of active cracks at a particular stress level, and this was expressed as an arbitrary 2-parameter Weibull distribution. Two new and efficient methods for calculating crack growth probabilities based on spherical triangles and spherical caps were developed. They utilized normalized stress coordinates and …


Static And Modal Analysis Of The Magnetic Levitation Vehicle, Santosh Kumar Desetty Apr 2005

Static And Modal Analysis Of The Magnetic Levitation Vehicle, Santosh Kumar Desetty

Mechanical & Aerospace Engineering Theses & Dissertations

The magnetic levitation train project at Old Dominion University has been stalled due to many technical problems. The control system is the main component of the vehicle, which is supposed to maintain an intended gap of 1 cm between the vehicle and the track while traveling, hence providing a smooth ride. The goal of the project is to document the mathematics of the complete system so that the control algorithm can be implemented and modified with the expectation of obtaining an improved levitation and propulsion.

The complete system includes the vehicle, the track, and the concrete guide-way. The focus of …


A Comparison Of Quasi-Static Indentation Testing To Low Velocity Impact Testing, Michael J. Douglas Apr 2000

A Comparison Of Quasi-Static Indentation Testing To Low Velocity Impact Testing, Michael J. Douglas

Mechanical & Aerospace Engineering Theses & Dissertations

A static test method for modeling low-velocity foreign object impact events to composites would prove to be very beneficial to researchers since much more data can be obtained from a static test than from an impact test. In order to examine if this is feasible, a series of static indentation and low velocity impact tests were carried out and compared. Square specimens of many sizes and thicknesses were utilized to cover the array of types of low velocity impact events. Laminates with a rt/4 stacking sequence were employed since this is by far the most common type of engineering laminate. …


Effect Of Temperature On Short-Term Creep Rupture Response In Polymer Matrix Pultruded Composites, Robert Harold Munson Jul 1999

Effect Of Temperature On Short-Term Creep Rupture Response In Polymer Matrix Pultruded Composites, Robert Harold Munson

Mechanical & Aerospace Engineering Theses & Dissertations

Polymer matrix pultruded composites have increasingly been used in applications where high strength-to-weight ratio and corrosion resistance are needed. Bridge and pier components are a couple of recent applications due the composite's resistance to corrosion from salt water. In applications of this sort, the material will commonly be subjected to sizable static loads while exposed to varying weather conditions. In using pultruded composites for these applications safely, a better understanding of the material's response to ambient conditions is necessary.

In this thesis, rectangular specimens of a polyester matrix glass reinforced pultruded composite sheet are subjected to both static tensile loading …


Large Amplitude Pitching Of Supermaneuver Delta Wings Including Flow Control, Yahia A. Abdelhamid Jul 1999

Large Amplitude Pitching Of Supermaneuver Delta Wings Including Flow Control, Yahia A. Abdelhamid

Mechanical & Aerospace Engineering Theses & Dissertations

The unsteady, three-dimensional Navier-Stokes equations are solved to simulate and study the aerodynamic response of a delta wing undergoing large amplitude pitching motion up to 90° angle of attack. The primary model under consideration consists of a 76° swept, sharp-edged delta wing of zero thickness, initially at zero angle of attack. The freestream Mach number and Reynolds number are 0.3 and 0.45 × 106, respectively. The governing equations are solved time-accurately using the implicit, upwind, Roe flux-difference splitting, finite-volume scheme. Both laminar and turbulent flow solutions are investigated. In the laminar flow solutions, validation of the computational results is carried …


An Experimental Investigation Into The Effect Of Clearance And Torque On Load Sharing In A Bolted Joint, Jerry B. Robertson Apr 1999

An Experimental Investigation Into The Effect Of Clearance And Torque On Load Sharing In A Bolted Joint, Jerry B. Robertson

Mechanical & Aerospace Engineering Theses & Dissertations

The shear load experienced by each bolt in a multi-fastener bolted butt joint is a percentage of the total load applied to the joint. Joint failure can be premature when one fastener is subjected to a disproportional amount of the total load. Conversely, the ultimate load the joint can endure may be increased if the distribution of loads can be equalized by some means. In this investigation, two and four fastener butt joints were studied. An instrumented bolt was constructed that could measure the bending stresses in the bolt associated with the bearing load. That data was converted into force …


Efficient Dynamic Unstructured Methods And Applications For Transonic Flows And Hypersonic Stage Separation, Xiaobing Luo Jan 1999

Efficient Dynamic Unstructured Methods And Applications For Transonic Flows And Hypersonic Stage Separation, Xiaobing Luo

Mechanical & Aerospace Engineering Theses & Dissertations

Relative-moving boundary problems have a wide variety of applications. They appear in staging during a launch process, store separation from a military aircraft, rotor-stator interaction in turbomachinery, and dynamic aeroelasticity.

The dynamic unstructured technology (DUT) is potentially a strong approach to simulate unsteady flows around relative-moving bodies, by solving time-dependent governing equations. The dual-time stepping scheme is implemented to improve its efficiency while not compromising the accuracy of solutions. The validation of the implicit scheme is performed on a pitching NACA0012 airfoil and a rectangular wing with low reduced frequencies in transonic flows. All the matured accelerating techniques, including the …


Design Optimization Of Magnetic Bearings And Magnetic Suspension Systems, V. Dale Bloodgood Jr. Oct 1998

Design Optimization Of Magnetic Bearings And Magnetic Suspension Systems, V. Dale Bloodgood Jr.

Mechanical & Aerospace Engineering Theses & Dissertations

Magnetic suspension systems were first demonstrated as practical by Holmes and Beams in the 1930's. Since then, numerous academic researchers have worked with various types of these systems. Commercial applications have largely been limited to magnetic bearings for rotating machinery. Other applications that have held considerable promise include wind tunnel model suspensions, space payload pointing and vibration isolation systems, satellite momentum storage and control devices and electromagnetic launch systems. However, none of these have progressed significantly beyond the prototype stage. Maglev trains have not reached serious commercial service but are being aggressively developed in Germany and Japan.

Design methods for …


Ir-Hot Gas Heat Source For Automated Tow Placement, Ray Walton Grenoble Apr 1998

Ir-Hot Gas Heat Source For Automated Tow Placement, Ray Walton Grenoble

Mechanical & Aerospace Engineering Theses & Dissertations

A series of five experiments on the NASA Langley automated tow placement robot revealed stagnation of gas flow in the nip region. Since the torches could not heat effectively in the nip region, the roller temperature was the dominant influence on interlaminar bond strength. The roller temperatures required for high bond strength caused resin and fiber on the panel top surface to adhere to the compaction roller. Resin and fiber was pulled from the panel surface and wrapped around the roller, which was a severe processing problem. A supplemental radiant heat source was designed to permit reductions in roller temperature. …


Placement Of Piezoelectric Actuators For Active Control Of Vibration Using Modal Parameters, Xuegeng Zhu Jan 1998

Placement Of Piezoelectric Actuators For Active Control Of Vibration Using Modal Parameters, Xuegeng Zhu

Mechanical & Aerospace Engineering Theses & Dissertations

An equation is derived to model the piezoelectric actuators incorporation with flexible structures. This equation permits the comparison of the performance indices over the entire structure for a piezoelectric actuator with constant area, which is unachievable if the Finite Element Method is used for complicated structures.

An index has been developed for placement of piezoelectric actuator for control of vibration of a flexible structure. This index is derived from the definition of H2norm. Computation of the proposed index requires only the natural frequencies and corresponding mode shapes of the structures of interest. The method is well suited to large …


Thermal And Mechanical Behavior Of Cryogenic Propellant Tank Concepts For Advanced Launch Vehicles, H. Kevin Rivers Oct 1997

Thermal And Mechanical Behavior Of Cryogenic Propellant Tank Concepts For Advanced Launch Vehicles, H. Kevin Rivers

Mechanical & Aerospace Engineering Theses & Dissertations

An important step in developing a cost-effective, fully-reusable, launch vehicle is the development of durable, lightweight, insulated, cryogenic propellant tanks. Current cryogenic tanks are expendable, and much of the technology that exist is not usable on future vehicles. As part of the Reusable Launch Vehicle/ X-33 Program, an experimental apparatus for evaluating the effects of both thermal and mechanical loading on cryogenic-tank concepts was developed at the NASA Langley Research Center. Studies to determine the behavior of various liquid-oxygen- and liquid-hydrogen-tank concepts under simulated mission conditions were performed as part of this research and are reported. Selected analytical studies of …


Research Related To Multi Degree Of Freedom Magnetic Suspensions, Yan Yang Jul 1997

Research Related To Multi Degree Of Freedom Magnetic Suspensions, Yan Yang

Mechanical & Aerospace Engineering Theses & Dissertations

This thesis covers the activities associated with 1) recommissioning of the 6-inch Magnetic Suspension and Balance System (MSBS) and 2) enhancing the Annular Suspension and Pointing System (ASPS). These activities continue the program of research in the multi degree of freedom magnetic suspension program at Old Dominion University. The 6-inch MSBS is a large gap magnetic suspension system used as a model support and balance system in wind tunnels. The first stage of recommissioning of the 6- inch MSBS for the 6-inch subsonic wind tunnel is performed. Experimental data and computational results for the magnetic field distribution of the MSBS …


Analysis And Testing Of Plates With Piezoelectric Sensors And Actuators, Jeffrey S. Bevan Apr 1997

Analysis And Testing Of Plates With Piezoelectric Sensors And Actuators, Jeffrey S. Bevan

Mechanical & Aerospace Engineering Theses & Dissertations

Piezoelectric material inherently possesses coupling between electrostatics and structural dynamics. Utilizing linear piezoelectric theory results in an intrinsically coupled pair of piezoelectric constitutive equations. One set describes the direct piezoelectric effect, where strains produce an electric field, and the other set describes the converse effect, where an applied electrical field produces strain. The purpose of this study is to compare the finite element analysis and experiments of a thin plate with bonded piezoelectric material.

Since an isotropic plate in combination with a thin piezoelectric layer constitutes a laminated composite, the classical laminate plate theory is used in the formulation to …


Development Of Curved-Plate Elements For The Exact Buckling Analysis Of Composite Plate Assemblies Including Transverse-Shear Effects, David Michael Mcgowan Apr 1997

Development Of Curved-Plate Elements For The Exact Buckling Analysis Of Composite Plate Assemblies Including Transverse-Shear Effects, David Michael Mcgowan

Mechanical & Aerospace Engineering Theses & Dissertations

The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. The formulation uses the principle of virtual work. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are then derived after the application of several simplifying assumptions. These equations are then modified to allow the reference surface of the plate to be located at a distance zc, from the centroidal surface. The implementation of the new theory into the …


An Experimental Investigation Of Bolt Preload Relaxation In Pultruded Gfrp Composite Joints, Srinivas Ravi Apr 1997

An Experimental Investigation Of Bolt Preload Relaxation In Pultruded Gfrp Composite Joints, Srinivas Ravi

Mechanical & Aerospace Engineering Theses & Dissertations

Mechanically fastened joints in pultruded composites are necessary for reasons of maintenance, repair, and assembly. Pultruded composites utilize polymers as matrices and therefore are susceptible to time-dependent effects. The positive effects of increasing the clamping force in bolted joints are well known. To maintain a safe operation of the assembly a minimum clamping force must be guaranteed. But since these materials show time-dependent effects, the bolt-preload relaxes over a period of time. The present study is aimed at investigating the bolt preload relaxation. In this study 1/2 in. thick pultruded sheets were first tested under compression in the thickness direction. …


Development And Experimental Verification Of A Finite Element Model For Ptc Panel Thermal Analysis, Hamid Sayar Oct 1996

Development And Experimental Verification Of A Finite Element Model For Ptc Panel Thermal Analysis, Hamid Sayar

Mechanical & Aerospace Engineering Theses & Dissertations

The Pyramidal Truss Core (PTC) panel is a new structural concept being used in applications requiring a high strength to weight ratio. This study is concerned with investigating the thermal characteristics of the PTC panels. In this regard, the focus of the analysis was to develop an accurate finite element model of PTC panels for thermal analysis. The resulting model included radiation mode of heat transfer as the dominant means of the heat transfer while neglecting the influence of heat transfer through natural convection. The accuracy of the developed model was verified by comparison of the finite element results with …


Effects Of Elevated Temperature On The Physical Aging Of A High Temperature Thermoplastic Resin And Composite, Mark Feldman Jul 1996

Effects Of Elevated Temperature On The Physical Aging Of A High Temperature Thermoplastic Resin And Composite, Mark Feldman

Mechanical & Aerospace Engineering Theses & Dissertations

Development of a High Speed Civil Transport is considered by the commercial aviation industry to be one of the next big challenges for our national aircraft industry. Critical to the success of this aircraft is the development of advanced polymeric composites for both the primary and secondary structures and the predictive methodology necessary for assessment of long term durability. While polymeric composites offer an excellent strength to weight ratio a key disadvantage is the time dependent properties exhibited by the polymer matrix which can age and ultimately effect the resultant stiffness of a laminate.

Experimental studies were performed to determine …


Progressive Failure Analysis Methodology For Laminated Composite Structures, David Wayne Sleight Jul 1996

Progressive Failure Analysis Methodology For Laminated Composite Structures, David Wayne Sleight

Mechanical & Aerospace Engineering Theses & Dissertations

A progressive failure analysis model has been developed for predicting the nonlinear response and failure of laminated composite structures. The progressive failure analysis uses C1 plate and shell elements based on classical lamination theory to calculate the in-plane stresses. Several failure criteria, including the maximum strain criterion, Hashin's criterion, and Christensen's criterion, are used to predict the failure mechanisms and several options are available to degrade the material properties after failures. The progressive failure analysis model is implemented in COMET and can predict the damage and response of a laminated composite structures from initial loading to final failure.


An Approach For Multidisciplinary Design Optimization, Robert V. Krueger Apr 1996

An Approach For Multidisciplinary Design Optimization, Robert V. Krueger

Mechanical & Aerospace Engineering Theses & Dissertations

Multidisciplinary Design Optimization (MDO) is an optimization technique that allows complex designs to be improved by managing conflicting goals in such a fashion so as to improve the overall design. This thesis presents a nonhierarchic MDO formulation and gives a general explanation of how it is to be applied to various appropriate problems. In addition, this thesis evaluates the viability of this MDO technique by applying it to two distinct, multidisciplinary problems that have been used as examples in other literature. The first example problem is a combined aerodynamic/structural problem and the second example is an alkylation process problem. First, …


Finite Element Formulation Of A Three-Node Spatially Curved And Twisted Beam, Umesh Vishnu Padhye Oct 1995

Finite Element Formulation Of A Three-Node Spatially Curved And Twisted Beam, Umesh Vishnu Padhye

Mechanical & Aerospace Engineering Theses & Dissertations

A three-node curved and twisted beam element is developed for linear analysis of structures modeled with curved and pre-twisted beams. A set of governing equations consisting of kinematic relations, constitutive relations, and equilibrium equations is derived. The beam element has three rotational and three displacement degrees of freedom at each node. The differential equations of kinematics are solved exactly for linearly varying longitudinal strains, constant transverse shear strains, linearly varying twist, and quadratically varying curvature changes to obtain the description of rotation and displacement modes. These rotation and displacement modes are then used as the basis functions for development of …


An Investigation Of Hole Size Effects In A Composite Material During Tensile Fracture, David Floyd Moore Apr 1995

An Investigation Of Hole Size Effects In A Composite Material During Tensile Fracture, David Floyd Moore

Mechanical & Aerospace Engineering Theses & Dissertations

An experimental investigation was conducted to evaluate the hole size effects, i.e., the reduction in strength with an increase in hole size at a constant stress concentration factor, for a glass fiber reinforced epoxy crossply laminate during tensile fracture. The characteristic dimension according to the point-stress and average-stress criteria of the two-parameter models proposed by Whitney and Nuismer were determined and compared for a circular hole, optimized circular hole, square hole with radiused corners and square hole with sharp corners. Modified versions of the two-parameter models proposed by Karlak and Pipes, Wetherhold, and Gillespie were also compared. On the basis …


Automatic Differentiation For First- And Second-Order Sensitivity Derivatives Of A Cfd Code, Laura Lee Sherman Apr 1995

Automatic Differentiation For First- And Second-Order Sensitivity Derivatives Of A Cfd Code, Laura Lee Sherman

Mechanical & Aerospace Engineering Theses & Dissertations

The straightforward automatic-differentiation and the hand-differentiated incremental iterative methods are interwoven to produce a hybrid scheme that captures some of the strengths of each strategy. With this compromise, discrete aerodynamic sensitivity derivatives are calculated with the efficient incremental iterative solution algorithm of the original flow code. Moreover, the principal advantage of automatic differentiation is retained (i.e., all complicated source code for the derivative calculations is constructed quickly with accuracy). The basic equations for second-order sensitivity derivatives are presented; four methods are compared. Each scheme requires that large systems are solved first for the first-order derivatives and, in all but one …


Modeling And Simulation Of Load Introduction For Fuselage Crown Panel Testing, Kevin P. Belack Apr 1995

Modeling And Simulation Of Load Introduction For Fuselage Crown Panel Testing, Kevin P. Belack

Mechanical & Aerospace Engineering Theses & Dissertations

This paper discusses the mechanism and behavior of load introduction to internally pressurized fuselage crown panels. Emphasis is placed on the finite element modeling of a simulated pressure-box test machine and representative fuselage crown panel. The geometry and mesh requirements for the finite element model are examined through numerical studies which gradually increase in complexity. These numerical studies culminate in the detailed specification of boundary conditions, mesh densities, load introduction mechanisms, element choice and solution process for the simulation of a pressure-box test machine and test panel.

The results obtained using the finite element model are then compared with experimental …


Development Of Vibration And Sensitivity Analysis Capability Using The Theory Of Structural Variations, Ting-Yu Rong Jul 1994

Development Of Vibration And Sensitivity Analysis Capability Using The Theory Of Structural Variations, Ting-Yu Rong

Mechanical & Aerospace Engineering Theses & Dissertations

In the author's previous work entitled "General Theorems of Topological Variations of Elastic Structures and the Method of Topological Variation," 1985, some interesting properties of skeletal structures have been discovered. These properties have been described as five theorems and synthesized as a theory, called the theory of structural variations (TSV). Based upon this theory, an innovative analysis tool, called the structural variation method (SVM), has been derived for static analysis of skeletal structures (one-dimensional finite element systems).

The objective of this dissertation research is to extend TSV and SVM from one-dimensional finite element systems to multi-dimensional ones and from statics …