Finite element method

This thesis is concerned with the analysis of the current distributions in coplanar parallel microstripline structures, and the calculation of crosstalk in these structures. This is accomplished by using a Finite Element Method approach. Two parallel strips, a right angle bend junction, and a T junction are studied in order to gain an insight into the current distributions and the primary causes of crosstalk. The control of crosstalk is also investigated, with alternative geometries for microstrip designs. It is seen that the finite element method can yield results comparable with other accepted methods, and other perceivable physical models of the test structures. Also shown in the present study that crosstalk can be reduced by decreasing the trace-to-ground plane separation.

A user friendly graphical interface was developed to control a Stewart platform which is a six degree-of-freedom in-parallel mechanism. The interface allows the user to define the platform motion relative to various coordinate systems: base, platform and joint. The velocity/position reference to the platform's controller can be provided by the following ways: preprogrammed data file, serial communication RS-232, 6 degrees of freedom joystick and soft teach pendant. The platform was designed to be used as "Space Emulator" and therefore a 6 degrees of freedom force/torque sensor was needed. Two different models of such sensors were designed and analyzed using finite element analysis techniques. Based on the results one particular model was selected, fabricated, instrumented with strain gages and calibrated in order to obtain its stiffness matrix. The effect of drifting of the sensor output due to self heating of the strain gages and the electronic components of the strain gage amplifiers was also studied.

Debond failures in structural sandwich may lead to severe reductions in load-bearing capability of the structure because of impartial transfer of shear and tensile forces between facing and core due to the lack of interfacial bonding. Analysis of interfacial bonding in sandwich specimens subjected to transverse tensile and shear forces is presented. Stress intensity factors computed based on the near-tip displacement field are related to experimental crack growth observation on the sandwich beams with aluminum skins on a wide range of PVC foam cores. Experimentally it was found that the crack tends to grow at the interface between the bondline and core as opposed to skin/bondline interface. In shear dominated fields, a pre-existing flow tended to deflect into the core rather than grow along the interface. The tendency for kinking and the direction of the kink is examined experimentally and analyzed using the finite element method.

This thesis deals with the static analysis of a three dimensional underwater acoustic tower exclusively designed and fabricated by Harbor Branch Oceanographic Institution, Ft. Pierce, Florida. A commercial finite element package COSMOS/M was used for the finite element analysis. The structural modeling as well as processing of the results was performed using GEOSTAR Ver. 1.65 interactive graphics package. The analysis was concentrated on the main instrument pipe carrying the required instruments for data acquisition. Various environmental loading induced by ocean currents, hydrostatic pressure, buoyancy and self weight of the tower have been considered in the analysis. The construction aspects of the tower as well as the finite element analysis of tower substructures are also discussed. The deflection of the tower due to the imposed loading is studied and deflection profiles are drawn.

A study of the stress distribution in and fracture behavior of the hermetic glass seal in a typical Integrated Circuit package is presented herein. Finite Element Analysis and Fracture Mechanics approaches were found effective for this investigation. A prescribed load or displacement applied at the tip of the lead protruding from the package causes high stresses at the lead-glass interface, which can lead to cracking and fracture of the seal. An approach for finding the value of the allowable load or displacement applicable at the lead tip is discussed. A correlation with a standard crack shape is presented for the 3-D model of the package. An extension of the problem revealing the effects of crack propagation on the stress intensity factor for the glass material is presented in later chapters. The J-integral method from Fracture Mechanics is found to be extremely useful for this investigation. A decline in the stress intensity factor with crack growth was observed from this study.

In this thesis, discretized finite element equations were derived and applied to the solution of electromagnetic fields in homogeneous and inhomogeneous waveguides. To improve the accuracy of the results several approaches were taken. Higher order elements were first introduced in the finite element formulation, then a penalty function was applied with explicit boundary conditions, which limit the appearance of nonphysical solutions. The results obtained from the finite element analysis were compared to analytical results when available and found to be very accurate.

This thesis develops a novel variable length cable model to simulate the behavior of submerged cables with variable unstretched length and a PC based simulation that integrates the governing cable equations. The general model is developed from continuous cable equations that are discretized using a finite element method with linear elements. Two systems of equations were developed, one for a variable length elastic element and the other for a constant length elastic element. A cable transition model is developed to ensure dynamic compatibility when a variable length element is divided or combined. The model proved to be an efficient and reliable tool to predict the behavior of underwater cables with variable length.

This work develops, a general numerical model and efficient integration routine to calculate the response of the underwater cable that connects the Lockheed Martin remote minehunting vehicle to its variable depth sensor. The general model is developed from continuous cable equations that are discretized using a finite element method with linear elements. The resulting discrete system of equations is nonlinear and stiff. Thus, we chose the implicit Generalized-alpha method to integrate these equations because it possess numerical dissipation. This integration routine is coded into a C++ based numerical simulation and the results and efficiency were compared with the results and efficiency of the Runge-Kutta method. Based on the validation test cases, Generalized-alpha method proved to be an efficient and reliable integration method for stiff equations governing the motion of underwater cables.

The behavior of radially polarized free-flooded ring (FFR) transducers is studied for application in underwater acoustic communications. Theoretical models are first presented. Then the finite element method (FEM) is introduced and a FEM model for the FFR transducer is proposed. Experimental data are collected and compared to the simulation results with good correspondence. A series of FEM simulations lead then to optimum geometrical parameters for a fine-tuned FFR transducer dedicated to underwater acoustic communications. Finally, stack transducers models and the piezocomposite technology are presented as possible improvement of the present transducer.

This dissertation deals with the non-perturbative finite element methods for stochastic structures and conditional simulation techniques for random fields. Three different non-perturbative finite element schemes have been proposed to compute the first and second moments of displacement responses of stochastic structures. These three methods are based, respectively, on (i) the exact inverse of the global stiffness matrix for simple stochastic structures; (ii) the variational principles for statically-determinate beams; and (iii) the element-level flexibility for general stochastic statically indeterminate structures. The non-perturbative finite element method for stochastic structures possesses several advantages over the conventional perturbation-based finite element method for stochastic structures, including (i) applicability to large values of the coefficient of variation of random parameters; (ii) convergence to exact solutions when the finite element mesh is refined; (iii) requirement of less statistical information than that demanded by the high-order perturbation methods. Conditional simulation of random fields has been an extremely important research field in most recent years due to its application in urban earthquake monitoring systems. This study generalizes the available simulation technique for one-variate Gaussian random fields, conditioned by realizations of the fields, to multi-variate vector random field, conditioned by the realizations of the fields themselves as well as the realizations of the fields derivatives. Furthermore, a conditional simulation for non-Gaussian random fields is also proposed in this study by combining the unconditional simulation technique of non-Gaussian fields and the conditional simulation technique of Gaussian fields. Finally, the dissertation incorporates the simulation technique of random field into the non-perturbation finite element method for stochastic structures, to handle the cases where only one-dimensional probability density function and the correlation function of the random parameters are available, the demanded two-dimensional probability density function is unavailable. Simulation technique is applied to generate the samples of random fields which are used to estimate the correlation between flexibilities over elements. The estimated correlation of flexibility is then used in finite element analysis for stochastic structures. For each proposed approach, numerous examples and numerical results have been implemented.