This thesis is primarily concerned with the development and coding of a Levy-type spectral plate element to analyze the harmonic response of simply supported plates in the mid to high frequency range. The development includes the governing PDE, displacement field, shape function, and dynamic stiffness matrix. A two DOF spectral Love bar element and both a four DOF spectral Euler-Bernoulli and a four DOF spectral Timoshenko beam element are also developed to gain insight into the performance of spectral elements. A cantilever beam example is used to show how incorporating eigenfunctions for the dynamic governing PDE into the displacement field enables spectral beam elements to represent the structural dynamics exactly. A simply supported curved beam example is used to show that spectral beam elements can converge the effects of curved geometry with up to a 50% reduction in the number of elements when compared to conventional FE. The curved beam example is also used to show that the rotatory inertia and shear deformation, from Timoshenko's beam theory, can result in up to a 28% shift in natural frequency over the first three bending modes. Finally, a simply supported Levy-plate model is used to show that the spectral Levy-type plate element converges the dynamic solution with up to three orders of magnitude fewer DOF then the conventional FE plate formulation. A simply-supported plate example problem is used to illustrate how the coefficients of the Fourier series expansion can be used as edge DOF for the spectral Levy-plate element. The Levy-plate element development gives insight to future research developing a general spectral plate element. / Master of Science

As the average American age increases, there is a need to study the spine biomechanics of adults with scoliosis. Most studies examining the mechanics of scoliosis have focused on in vitro testing or computer simulations, but in vivo testing of the mechanical response of a scoliotic spine has not yet been reported. The purpose of this study was to quantitatively define the passive stiffness properties of the in vivo scoliotic spine in three principle anatomical motions and identify differences relative to healthy controls. Scoliotic (n=14) and control (n=17) participants with no history of spondylolisthesis, spinal fracture, or spinal surgery participated in three different tests (torso lateral side bending, torso axial rotation, and torso flexion/extension) that isolated mobility to the in vivo lumbar spine. Scoliotic individuals with Cobb angles ranging 15-75 degrees were accepted. Applied torque was measured using a uni-directional load cell, and inertial measurement units (IMU) recorded angular displacement of the upper torso relative to the pelvis and lower extremities. Torque-rotational displacement data were fit using a double sigmoid function, resulting in excellent overall fit (R2 > 0.901). The neutral zone (NZ) width, or the range of motion where there is minimal internal resistance, was then calculated. Stiffnesses within the NZ and outside of the NZ were also calculated. Stiffness asymmetries were also computed within each trial. These parameters were statistically compared between factor of population and within factor of direction. There was an interaction effect between populations when comparing axial twist NZ width and lateral bend NZ width. The lateral bend NZ width magnitude was significantly smaller in scoliotic patients. NZ stiffness in the all three directions was greater in the scoliotic population. There was no significant difference in asymmetrical stiffness between populations. The present study is the first investigation to quantify the in vivo neutral zone and related mechanics of the scoliotic lumbar spine. Future research is needed to determine if the measured lumbar spine mechanical characteristics can help explain progression of scoliosis and complement scoliosis classification systems. / Master of Science

The aim of this thesis is the stiffness analysis of cable-driven parallel robots. Cable-driven parallel robots have drawn considerable attention because of their unique abilities and advantages such as the large workspace, light weight of cable actuators, easy disassembly and transportation of the robot. The mobile platform of a cable-driven parallel robot is attached to the base with multiple cables. One of the parameters that should be studied to make sure a robot is able to execute a task accurately is stiffness of the robot. In order to investigate the stiffness behaviour of a robot, the stiffness matrix can be calculated as the first step. Because cables act in tension, keeping the positive tension in cables becomes a challenge. In order to have a fully controllable robot, an actuation redundancy is needed. These complexities are addressed in the thesis and simulations. In this thesis, the complete form of the stiffness matrix is considered without neglecting any terms in calculation of the stiffness. Some stiffness indices such as single-dimensional stiffness based on stiffness ellipse, directional stiffness and condition number of the stiffness matrix are introduced and calculated and stiffness maps of the robot are developed. In addition, the issue of unit inconsistency in calculating the stiffness index is addressed. One of the areas which is also addressed in this thesis is failure analysis based on the stiffness of robot. The effect of the failure in one or more cables or motors is modelled and stiffness maps are developed for the failure situation. It is shown that by changing the anchor position and mobile platform orientation, the lost stiffness after failure of a cable or motor can be retrieved partially. Optimum anchor position and mobile platform orientation are identified to maximize the area of the stiffness map. Condition number of the stiffness matrix while robot is following a trajectory is optimized. In addition, when one cable fails during the path planning, the recovery of the robot is studied. Finally, these analyses on stiffness and failure provide the designer with the necessary and valuable information about the anchor positions and actuator toques. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2013-04-27 08:47:26.297

An experimental investigation was conducted to study the stiffness of wood diaphragms. Currently there is no method to calculate wood diaphragm stiffness that can reliably account for all of the various framing configurations. Diaphragm stiffness is important in the design of wood framed structures to calculate the predicted deflection and thereby determine if a diaphragm may be classified as rigid or flexible. This classification controls the method by which load is transferred from the diaphragm to the supporting structure below. Multiple nondestructive experimental tests were performed on six full-scale wood diaphragms of varying sizes, aspect ratios, and load-orientations. Each test of each specimen involved a different combination of construction parameters. The construction parameters investigated were blocking, foam adhesive, presence of designated chord members, corner and center sheathing openings, and presence of walls on top of the diaphragm. The experimental results are analyzed and compared in terms of equivalent viscous damping, global stiffness, shear stiffness, and flexural stiffness in order to evaluate the characteristics of each construction parameter and combinations thereof. Recommendations are presented at the end of this study as to the next steps toward development of an empirical method for calculating wood diaphragm stiffness. / Master of Science

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This thesis presents an evolutionarily design change for the Delta parallel robot. The proposed design change increases the useful workspace of the robot and aids in permanently avoiding singularities in the workspace. This is accomplished by means of a new intermediate link parallel to the 4 bar linkage. The addition of the new link simultaneously increases the total workspace volume and decreases the dexterity without significantly affecting the stiffness. The design is analyzed and the inverse kinematics, Jacobian, sti ness and dexterity relations are formulated. The relations are then converted into a form that is usable by MATLAB to calculate di erent workspaces that illustrate the advantages of the new design. Subsequently, an optimization problem is formulated that aims to take advantage of the new attributes to create a balanced robot that further illustrates the benefits of the new design. The results are clearly illustrated by comparing plotted sections of workspace from both the optimized and unoptimized workspace. Lastly, the design is developed into a 3D model which is then fabricated into a working prototype to test and verify functionality. / UOIT

This report is the documentation for a stiffness formulation to perform rigid diaphragm analysis for wood structures subjected to wind loads. Traditionally, rigid diaphragm analysis has been performed using a vaguely-defined superposition approach; however, this report details a more rational stiffness approach to solving for forces placed on walls resulting from a rigid diaphragm, and its implementation is via a simple spreadsheet application. In addition to the formulation of the spreadsheet, the report contains a User’s Guide and examples of the spreadsheet’s use. The purpose of the spreadsheet is not as a replacement to more sophisticated and comprehensive finite element analysis software, but as a tool to aid designers who practice engineering and may not have access to such software. In general, the application is developed for wood diaphragms as will be noted by references to wood-related codes. However, much of the approach may be used for diaphragms constructed with other materials as well. / text