This dissertation developed a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. As a proof of concept, a joint 2D-beam approach is studied for planar-inplane deformation of strip-beams. This approach is developed for obtaining understanding needed to do the joint 3D-beam model. A Matlab code is developed to solve achieve this 2D-beam approach. For joint 2D-beam approach, the static response of a basic 2D-beam model is studied. The whole beam structure is divided into two parts. The root part where the boundary condition is applied is constructed as a 2D model. The free end part is constructed as a beam model. To assemble the two different dimensional model, a transformation matrix is used to achieve deflection continuity or load continuity at the interface. After the transformation matrix from deflection continuity or from load continuity is obtained, the 2D part and the beam part can be assembled together and solved as one linear system. For a joint 3D-beam approach, the static and dynamic response of a basic 3D-beam model is studied. A Fortran program is developed to achieve this 3D-beam approach. For the uniform beam constrained at the root end, similar to the joint 2D-beam analysis, the whole beam structure is divided into two parts. The root part where the boundary condition is applied is constructed as a 3D model. The free end part is constructed as a beam model. To assemble the two different dimensional models, the approach of load continuity at the interface is used to combine the 3D model with beam model. The load continuity at the interface is achieved by stress recovery using the variational-asymptotic method. The beam properties and warping functions required for stress recovery are obtained from VABS constitutive analysis. After the transformation matrix from load continuity is obtained, the 3D part and the beam part can be assembled together and solved as one linear system. For a non-uniform beam example, the whole structure is divided into several parts, where the root end and the non-uniform parts are constructed as 3D models and the uniform parts are constructed as beams. At all the interfaces, the load continuity is used to connect 3D model with beam model. Stress recovery using the variational-asymptotic method is used to achieve the load continuity at all interfaces. For each interface, there is a transformation matrix from load continuity. After we have all the transformation matrices, the 3D parts and the beam parts are assembled together and solved as one linear system.

Heatshield design and analysis has traditionally been a decoupled process, the designer creates the geometry generally without knowledge about how the design variables affect the thermostructural response or how the system will perform under off nominal conditions. Heatshield thermal and structural response analyses are generally performed as separate tasks where the analysts size their respective components and feedback their results to the designer who is left to interpret them. The analysts are generally unable to provide guidance in terms of how the design variables can be modified to meet geometric constraints and not exceed the thermal or structural design specifications. In general, the thermal response analysis of ablative thermal protection systems has traditionally been performed using a one-dimensional finite difference calculation. The structural analyses are generally one, two, or three-dimensional finite element calculations. In this dissertation, the governing differential equations for ablative thermal response are solved in three-dimensions using the finite element method. Darcy' Law is used to model the flow of pyrolysis gas through the ablative material. The three-dimensional governing differential equations for Darcy flow are solved using the finite element method as well. Additionally, the equations for linear elasticity are solved by the finite element method for the thermal stress using temperatures directly from the thermal response calculations. This dissertation also links the analysis of thermal protection systems to their design. The link to design comes from understanding the variation in the thermostructural response over the range of the design variables. Material property sensitivities are performed and an optimum design is determined based on a deterministic analysis minimizing the design specification of bondline temperature subject to appropriate constraints. A Monte Carlo simulation is performed on the optimum design to determine the probability of exceeding the design specifications. The design methodology is demonstrated on the Orion Crew Exploration Vehicle's compression pad design.

Surface-breaking cracks pose a serious threat to the service life of concrete structures and health monitoring is presently conducted by a visual inspection method, yielding a potential risk to safety. Diffuse ultrasonic techniques have shown their potential as an ultrasonic technique for measuring crack depth in concrete and are currently under development. In this research, the finite element method (FEM) is employed to model the ultrasound diffusion in a concrete specimen. The objectives are to use the commercial finite element (FE) tool Ansys to develop the finite element model of a concrete specimen and verify the applicability of the model by comparing with an analytic solution and experiment data. Further, various crack types are analyzed with the FE model in order to gain physical insight into the interpretation of experimental measurements. The results of this research suggest that a preliminary knowledge of the cracking process is required to correctly interpret the measured impulse responses for an unknown crack geometry, as the impulse response expresses the response of the shortest path through a system of cracks between source and receiver. Moreover, the impulse response can carry some ambiguity, as certain crack types are not uniquely determined.

This thesis focuses on the finite element modeling and analysis of wood shoring towers used by Urban Search and Rescue (US&R) teams during emergency response situations. These shores are constructed on site to provide temporary stabilization to a damaged structure. A high demand exists for experimental testing of the performance of these shores under non-ideal loading conditions, and for possible design modifications that could improve their overall behavior. To respond to this need, a total of thirteen vertical shores of the type laced post (LP) and plywood laced post (PLP) were constructed and tested at the Ferguson Structural Engineering Laboratory (FSEL) in Austin, Texas. The tests conducted on these shores aimed to investigate their performance under purely vertical load as well as various combinations of vertical and lateral loads. Finite element models for eight of the shores tested at FSEL were built and analyzed in Abaqus to compare the computed results with the actual linear elastic response of the shores. Material properties for the posts in each shore were obtained through further material testing at the conclusion of each shore test. Shore members were assumed to be isotropic. Solid elements were used to model each member, and Cartesian connector elements with a predefined nonlinear stiffness were used to model each nail. In general, the vertical load-displacement response computed from Abaqus exhibited good agreement with the laboratory results for the linear elastic range. The same general modeling scheme was then used to make design changes to the original shores based on observations gained during testing as well as modeling. Each design change was modeled, analyzed, and then compared with the computed results from the original shore design as well as the other design changes. The basis for evaluating the effectiveness of a given shore design involved comparing the bending moment diagrams for each post and the maximum first story nail slips (connector displacements). Recommendations were made for improved shore designs to be verified by experimental testing. / text

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Femoroacetabular impingement (FAI) is recognized as a pathomechanical process that leads to hip osteoarthritis (OA). It is hypothesized that mechanical stimuli are prominent at higher range of motions in hips with cam FAI (aspherical femoral head-neck deformity). Adverse loading conditions can impose elevated mechanical stimuli levels at the articulating surfaces and underlying subchondral bone, which plays a predominant mechanical role in early OA. The aim of this research was to determine the levels of mechanical stimuli within the hip, examining the effects of severe cam impingement on the onset of OA, using patient-specific biomechanics data, CT data, and finite element analysis (FEA). Patient-specific hip joint reaction forces were applied to two symptomatic patient models and two control-matched models, segmented from patient-specific CT data. The finite element models were simulated to compare the locations and magnitudes of mechanical stimuli during two quasi-static positions from standing to squatting. Maximum-shear stress (MSS) was analyzed to determine the adverse loading conditions within the joint and strain energy density (SED) was determined to examine its effect on the initiation of bone remodelling. The results revealed that peak mechanical stimuli concentrations were found on the antero-superior acetabulum during the squatting position, underlying to the cartilage. The MSS magnitudes were significantly higher and concentrated for the FAI patients (15.145 ± 1.715 MPa) in comparison with the MSS magnitudes for the control subjects (4.445 ± 0.085 MPa). The FAI group demonstrated a slight increase in peak SED values on the acetabulum from standing (1.005 ± 0.076 kPa) to squatting (1.018 ± 0.082 kPa). Insignificant changes in SED values were noticed for the control subjects. Squatting orients the femoral head into the antero-superior acetabulum, increasing the contact area with the cartilage and labral regions, thus resulting in higher peaks behind the cartilage on the acetabulum. The resultant location of the peak MSS and SED concentrations correspond well with the region of initial cartilage degradation and early OA observed during open surgical dislocation. Due to the relatively low elastic modulus of the articular cartilage, loads are transferred and amplified to the subchondral bone. This further suggests that elevated stimuli levels can provoke stiffening of the underlying subchondral plate, through bone remodelling, and consequently accelerating the onset of cartilage degradation. Since mechanical stimuli results are unique to their patient-specific loading parameters and conditions, it would be difficult to determine a patient-specific threshold to provoke bone remodeling at this stage.

Thesis (M.App.Sc.) - Carleton University, 2002. / Includes bibliographical references (p. 90-94). Also available in electronic format on the Internet.

Often bone fractures are joined by inserting metal plates and screws to hold the fragmented bone under compression. However, after the fractured bone is healed removing the screws leaves holes in the bone which takes months to fill up and heal completely. The goal of this research is to investigate those voids specifically in a finite element model of a femur. The holes were found to experience high stress that can easily lead to crack propagations during everyday activities. Finite element models of femurs were modeled after two common fracture fixation systems, specifically just after the plates, rods and screws are removed. To observe the stress levels bones are likely to experience, common mechanical tests that are relevant to or associated with common daily activities were performed. While the 3-point bending tests did not yield significant results, the compression and torsion tests produced high stress areas near the screw holes. In certain cases, the von Mises’ stress reached 3.66 x 106 N/mm2. Our finite element modeling seeks to establish groundwork for future explorations on the holes created by fracture fixation hardware. In the future, this work will lead to redesigning of fixation systems with reduced stress concentration around the holes. Therefore, the initiation of new cracks around these holes will be limited during everyday activity.

The purpose of this paper is to develop a general method for using Finite Elements in the Steepest Descent Method. The main application is to a partial differential equation for a Transonic Flow Problem. It is also applied to Burger's equation, Laplace's equation and the minimal surface equation. The entire method is tested by computer runs which give satisfactory results. The validity of certain of the procedures used are proved theoretically. The way that the writer handles finite elements is quite different from traditional finite element methods. The variational principle is not needed. The theory is based upon the calculation of a matrix representation of operators in the gradient of a certain functional. Systematic use is made of local interpolation functions.

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