A first-order shear deformation plate theory is used to predict free vibration frequencies in rotating laminated composite plates. The theory accounts for geometric non-linearity in the form of von Karman strains. The plate is permitted to have arbitrary orientation and offset from the axis of rotation. A finite element model is developed to obtain a solution to the problem. The model is validated by comparing the results for free vibration of non-rotating plates for various boundary conditions and material properties with the exact results based on the classical plate theory and the first-order shear deformable plate theory. Results are presented for free vibration of isotropic and laminated composite plates rotating at different angular velocities. A study has also been made on the change in the free vibration frequencies of the plate with angular velocity for different plate thicknesses and for different modulus ratios. / Master of Science

Described is a development of a new finite element-method-based numerical technique to carry out the steady-state thermal analysis of a cylindrical electric furnace. Such furnaces are in common use for the continuous melting of glass rods. Our aim was to use an iterative technique in which components of the furnace were visited sequentially and which would require less memory and would serve as an alternative to creating a global matrix encompassing the entire solution domain. A finite element method code was written in C++ to accomplish this. The code was first used in a test case involving a thermally connected system consisting of three cylindrical sectors. Then upon running the code for a full furnace assembly it was found that although the approach was valid, the iterative technique took much longer to converge than had been anticipated. Attempts were made to speed up the convergence and to reduce the time required for executing a single iteration. While some modest improvement was achieved, convergence could not be speeded up to a sufficient degree to make this new approach practical using current generation computers. It was concluded from this research that though the new approach is theoretically valid, it can not be practically implemented until significant improvements in machine speed or new, more efficient algorithms are available. The new approach, however, is a viable option for users who have time to wait for a converged solution but who do not have the resources to buy an expensive workstation. / Master of Science

The main objectives of the present study are to incorporate Saint-Venant's torsion solution in the analysis of a glulam dome with ABAQUS to include warping of rectangular beams, and to model the nonlinear beam/decking connectors (nails) of the dome in order to develop an effective finite element model of the glulam dome for investigating its ultimate load capacity. The shear modulus is modified to include warping of the beams. The nonlinear connector is defined through a user-coded FORTRAN subroutine UEL. Results from the thorough testing of these two capabilities are presented. A convergence study of the solution in the nonlinear analysis of the dome cap with ABAQUS is performed. The effect of variation in parameters such as the nonlinear material law and the stiffness of hinge-connector elements on the dome cap model is examined. A dome cap model with 16 nailed joints for each beam is analyzed. Dome models with nailed joints at truss bracing points (i.e., the end nodes of the truss bracing elements) and with 16 nailed joints for every beam are analyzed. The results of these models are compared with the models with and without truss bracing. Finally, conclusions based on this study and recommendations for future research are presented. / Master of Science

The wealth of experimental laser data and its high accuracy allow a rigorous comparison between a distributed model and distributed measurements that was not possible previously. The purpose of this work is to obtain and compare experimental and analytical distributed measurements for a simple structure excited by a point force (from a shaker) and by a distributed force (from a single or pair of piezoceramic actuators). The analytical results are obtained from the forced response analysis of a finite element model. A known piezoelectric actuator model that shows the actuation effects produced by symmetrically bonded actuators are line moments along the edges of the actuator and the effects produced by a single actuator are line moments and forces along its edges is used. A forced response analysis is performed on this model and the amplitude of the sinusoidal displacement at each prescribed point along the structure is found. Experimentally, a scanning laser vibrometer is used to measure the velocity along the structure due to the hannonic excitations. The vibration amplitudes are found from these results and compared to the modeling results. The predicted displacement shapes for the various excitations and boundary conditions resemble the measured shapes. The exact magnitudes of the predicted displacements along the beam do not corroborate the experimental results. The differences between the two are inconsistent over the length and width of the beam and over the excitation frequencies considered. Various modeling and experimental reasons are cited for this inaccuracy. The other moments from the edges of the piezoceramic actuators parallel to the length of the beam are found to influence the beam response even at low frequencies. The laser measures some torsional effects in the beam that are not predicted by the model. The measured responses show that at high excitation frequencies mode shapes indicative of a plate are excited in the beam by the piezoceramic actuators. / Master of Science

In high-frequency power transformers, magnetic material properties cannot be assumed to be constant. These properties vary with frequency, temperature, and magnetic flux density. Heat generation is, in turn, a function of the magnetic permeability, magnetic flux density, and frequency. Current design methods are either empirical or based on linear, uncoupled models. To better understand the relationship between heat transfer, magnetic flux density, material properties, and core geometry in a miniature, high-frequency transformer, a finite-element program has been developed to solve the coupled thermal-magnetic equations for an axisymmetric transformer. The program accounts for nonlinear temperature and magnetic field dependent material properties, geometry, and driving frequency. The program, HT-MAG, is based on a series of derived magnetic field equations. The Ritz method is applied to the magnetic and thermal equations in the development of the program. The program alternately solves the finite element approximations to the thermal and magnetic governing equations until the magnetic properties match within a specified fraction or a maximum number of iterations are performed. In addition, the program can be linked with existing pre- and post-processors or can accept manual pre- and post-processing. Six test cases were run to test the validity of the program. The first two cases tested the uncoupled heat transfer calculations. One of these tested the thermal conduction calculations while the other tested the heat generation calculations. The next two cases tested the uncoupled magnetic equations. The first was a direct current (DC) case, while the second was an alternating current (AC) case. The final two cases tested the thermal magnetic coupling. Solutions to these cases are presented and discussed. / Master of Science

The study involves the development of a finite element model of a hermetic reciprocating compressor for noise prediction applications. Inherent difficulties in developing the finite element model of a complicated structure are discussed and appropriate modeling strategies are evolved. The development of the complete compressor finite element model is carried out in two stages - modeling of the compressor housing and the assembly of components into the compressor assembly. The compressor housing is isolated for detailed modeling. Geometry complexity, secondary masses, spring mounts, lap-joint and manufacturing variations pose challenges in developing a reliable model. Frequent comparisons are made with experimental mobility scans to obtain insights into the actual behavior of the modeled structure. When possible, weaknesses are located in the finite element model and corrected. After sufficient revisions, 23 natural frequencies (excluding the rigid body modes) are found for the compressor housing in the low frequency range (below 2000 Hz) of analysis. Forced response calculations are also used to correlate the analytical model and test data, with a maximum of 5% disagreement for the 14 natural frequencies that could be correlated. Compressor assembly modeling involves detailed solid modeling of internal components for inertia properties, developing reduced-degrees-of-freedom models of mounting springs and modeling of the shockloop. The dynamic behavior of the crankcase is investigated separate from the compressor assembly model. Finally, the components are assembled and the compressor assembly is solved for its natural frequencies by the component mode synthesis method. Eighty seven natural frequencies below 2000 Hz (excluding the rigid body modes) are found for the compressor assembly model. This model can be used to predict velocity responses on the surface of the housing, with the internally generated forces as excitations. Velocity response data are directly used in sound prediction. / Master of Science

Two prominent continuum mechanics based incremental nonlinear finite element formulations are reviewed. An introduction to different material response measures suitable for nonlinear analysis, in addition to an overview of the Total and Updated Lagrangian reference frames, serve as the starting point for this review. The two nonlinear formulations are specialized for use with a geometrically nonlinear plane truss finite element. The truss formulations are then implemented into separate geometrically nonlinear finite element codes. Numerical comparisons of five test structures are carried out using ABAQUS and both programs. ABAQUS serves as the bench-mark by which the solution accuracy of the two programs is judged. / Master of Science / incomplete_metadata

The thesis presents a three dimensional shape optimization program which analyzes models made up of linear isoparametric elements. The goal of the program is to achieve a near uniform model stress state and thereby to minimize material volume. The algorithm is iterative, and performs two analyses per iteration. The first analysis is a static stress analysis of the model for one or more load cases. Based on results from the static analysis, an expansion analysis is performed. Model elements are expanded or contracted based on whether they are stressed higher or lower than a reference stress. The shape changing is done by creating an expansion load vector using the differences between the calculated element stresses and the reference stress. Expansion displacements are solved for, and instead of using them to calculate stresses, the displacements are added to the nodal coordinates to reshape the structure. This process continues until a user defined convergence tolerance is met. Four programs were used for the analysis process. Models were created using a finite element modeling program called I-IDEAS or CAIEDS. The I-IDEAS output files were converted to input files for the optimizer by a conversion program. The model was optimized using the shape optimization process described above. Post- processing was done using a program written with a graphical programming language called graPHIGS. Models used to test the program were: a cylindrical pressure vessel with nonuniform thickness, a spherical pressure vessel with non-uniform thickness, a torque arm, and a draft sill casting o a railroad hopper car. Results were compared to similar studies from selected references. Both pressure vessels converged to near uniform thicknesses, which compared ell with the reference work. In a two dimensional analysis, the torque arm volume decreased 24 percent, which compared well with published results. A three dimensional analysis showed a volume reduction of l3 percent, but there were convergence problems. Finally, the draft sill casting was reduced in volume by 9 percent from a manually optimized design. / Master of Science

In this thesis, we study the static and free vibration response of symmetric and antisymmetric cross-ply laminated plates using different plate theories. Governing equations for two displacement-based third-order equivalent-single-layer theories have been developed. The first one is called the General Third-Order Theory (GTOT), and the second one is called the General Third-Order Theory of Reddy (GTTR). The displacement field of the second theory can be obtained from the first by imposing the condition of zero shear stresses at the bounding planes of the plate. The governing equations, analytical solutions, and finite element model of GTTR have been obtained in terms of tracers. Proceeding in this manner, the governing equations, analytical solutions, and finite element models of some lower-order plate theories fall out by just assigning appropriate values to the tracers (typically 1 or 0). While analytical and finite element solutions have been obtained for GTTR and its derivative cases, only finite element solutions have been obtained for GTOT. The analytical solutions are of two types. The Navier-type solution is for rectangular plates simply supported on all four edges. In the Levy-type solution, two sides of the plate have to be simply-supported, while the remaining two sides can have any combination of free, clamped, or simply-supported boundary conditions. The results obtained from the different theories have been compared with exact solutions from existing literature . The response characteristics of the plates, like deflections, stresses, and frequencies, as well as the parameters affecting them have been studied. Some of the parameters investigated are span-to-thickness ratios, boundary conditions, loadings, and lamination schemes. The performance of the different theories in predicting plate responses have been evaluated. / Master of Science

Relatively new transducers permit the measurement of dynamic response at many structure locations. Included among such transducers is the scanning laser Doppler vibrometer (LDV). A scanning LDV can measure velocity at many structure locations. An important new technique, Experimental Spatial Dynamics Modeling (ESDM), utilizes such spatially dense velocity data. ESDM models continuous, three-dimensional velocity fields using LDV velocity data. Thus, ESDM is a powerful structural dynamics analysis tool that significantly enhances the usefulness of a scanning LDV. However, heretofore, ESDM has not been experimentally evaluated. The results contained herein partially satisfy this need. Specifically, this research evaluated the ability of ESDM to reconstruct velocity response fields with large in-plane components parallel to a surface in the presence of small out-of-plane components transverse to the surface. To fulfill this objective, a test structure was developed and fabricated; the structure had certain dynamic properties which aided ESDM evaluation. Subsequently, the test structure was harmonically excited at a single frequency such that large in-plane and small out-of-plane velocity components were present on a particular surface. LDV and accelerometer data were then collected. Ultimately, velocity results were obtained from the LDV data via ESDM and the accelerometer data. Velocity results derived from the accelerometer data served as an experimental standard against which ESDM results were compared. Result comparisons clearly indicate that ESDM accurately reconstructs surface velocity fields with large in-plane and small out-of-plane components. / Master of Science