This research investigation explores the feasibility of implementing a laser welded sandwich steel panel bridge deck system as a viable alternative to standardized reinforced concrete bridge decks. Generally used in naval ship building applications, steel sandwich panels possess attractive characteristics towards the integration with bridge infrastructure such as service life in excess of 100 plus years, dead load reduction, rapid construction, decreased closure time, and automated mass production. The lack of fatigue data for the laser "stake" welds used to create the enclosed sandwich panel geometry raised concerns with respect to fatigue life. The primary focus of this study was to determine whether or not infinite fatigue life was possible. Two different laser welding technologies were investigated, Laser Beam Welding (LBW) and Hybrid-Laser Arc Welding (HLAW). Test specimens were fabricated and tested in order to examine fatigue resistance based on a localized load effect between adjacent core stiffeners. Finite element models were used to obtain the stress range for each individual test due to complex geometry and partially restrained boundary conditions. In order to assess the fatigue performance of the overall deck system, additional finite element models were created to study the local and global behavior of different sandwich panel configurations. As a whole the investigation yielded promising results. Infinite fatigue life is achievable due to outstanding fatigue performance. The HLAW stake welds demonstrated superior fatigue resistance in comparison to the LBW process. Localized load effects can be minimized through the modification of different panel parameters. Pushing forward, full scale testing is essential to the future employment of this innovative bridge deck system. / Master of Science

Finite element modeling has become a powerful tool in orthopedic biomechanics, allowing simulations with complex geometries. Current fatigue behavior simulations are unable to accurately predict the cycles to failure, creep, and damage or modulus loss even when applied to a bending model. It is thought that the inhomogeneity of the models may be the source of the problem. It has also been suggested that the volume size of the element will affect the fatigue behavior. This is called a stressed volume effect. In this thesis non-homogeneous finite element models were used to examine the effects of "sizing factors" on damage laws in fatigue simulations. Non-homogeneous finite element models were created from micro computed tomography (CT) images of dumbbell shaped fatigue samples. An automatic voxel meshing technique was used which converted the CT data directly into mesh geometry and material properties. My results showed that including these sizing factors improved the accuracy of the fatigue simulations on the non-homogeneous models. Using the Nelder-Mead optimization routine, I optimized the sizing factors for a group of 5 models. When these optimized sizing factors were applied to other models they improved the accuracy of the simulations but not as much as for the original models, but they improved the results more than with no sizing factors at all. I found that in our fatigue simulations we could account for the effects of stressed volume and inhomogeneity by including sizing factors in the life and damaging laws. / Master of Science

This thesis develops an immersed finite element (IFE) space for numerical simulations arising from beam design with multiple materials. This IFE space is based upon meshes that can be independent of interface of the materials used to form a beam. Both the forward and inverse problems associated with the beam equation are considered. The order of accuracy of this IFE space is numerically investigated from the point of view of both the interpolation and finite element solution of the interface boundary value problems. Both single and multiple interfaces are considered in our numerical simulation. The results demonstrate that this IFE space has the optimal order of approximation capability. / Master of Science

Thesis: B.S., Massachusetts Institute of Technology, Department of Mechanical Engineering, 1978 / Includes bibliographical references. / by Arthur P. Cimento. / B.S. / B.S. Massachusetts Institute of Technology, Department of Mechanical Engineering

A direct solution procedure is proposed and developed which exploits the parallelism that exists in current symmetric multiprocessing (SMP) multi-core processors. Several algorithms are proposed and developed to improve the performance of the direct solution of FE problems. A high-performance sparse direct solver is developed which allows experimentation with the newly developed and existing algorithms. The performance of the algorithms is investigated using a large set of FE problems. Furthermore, operation count estimations are developed to further assess various algorithms. An out-of-core version of the solver is developed to reduce the memory requirements for the solution. I/O is performed asynchronously without blocking the thread that makes the I/O request. Asynchronous I/O allows overlapping factorization and triangular solution computations with I/O. The performance of the developed solver is demonstrated on a large number of test problems. A problem with nearly 10 million degree of freedoms is solved on a low price desktop computer using the out-of-core version of the direct solver. Furthermore, the developed solver usually outperforms a commonly used shared memory solver.

A triangular B-spline (DMS-spline)-based finite element method (TBS-FEM) is proposed along with possible enrichment through discontinuous Galerkin, continuous-discontinuous Galerkin finite element (CDGFE) and stabilization techniques. The developed schemes are also numerically explored, to a limited extent, for weak discretizations of a few second order partial differential equations (PDEs) of interest in solid mechanics. The presently employed functional approximation has both affine invariance and convex hull properties. In contrast to the Lagrangian basis functions used with the conventional finite element method, basis functions derived through n-th order triangular B-splines possess (n ≥ 1) global continuity. This is usually not possible with standard finite element formulations. Thus, though constructed within a mesh-based framework, the basis functions are globally smooth (even across the element boundaries). Since these globally smooth basis functions are used in modeling response, one can expect a reduction in the number of elements in the discretization which in turn reduces number of degrees of freedom and consequently the computational cost. In the present work that aims at laying out the basic foundation of the method, we consider only linear triangular B-splines. The resulting formulation thus provides only a continuous approximation functions for the targeted variables. This leads to a straightforward implementation without a digression into the issue of knot selection, whose resolution is required for implementing the method with higher order triangular B-splines. Since we consider only n = 1, the formulation also makes use of the discontinuous Galerkin method that weakly enforces the continuity of first derivatives through stabilizing terms on the interior boundaries. Stabilization enhances the numerical stability without sacrificing accuracy by suitably changing the weak formulation. Weighted residual terms are added to the variational equation, which involve a mesh-dependent stabilization parameter. The advantage of the resulting scheme over a more traditional mixed approach and least square finite element is that the introduction of additional unknowns and related difficulties can be avoided. For assessing the numerical performance of the method, we consider Navier’s equations of elasticity, especially the case of nearly-incompressible elasticity (i.e. as the limit of volumetric locking approaches). Limited comparisons with results via finite element techniques based on constant-strain triangles help bring out the advantages of the proposed scheme to an extent.

In this dissertation, we explore applications of partial differential equations with discontinuous coefficients. We consider the nonconforming immersed finite element methods (IFE) for modeling and simulating these partial differential equations. A one-dimensional second-order parabolic initial-boundary value problem with discontinuous coefficients is studied. We propose an extension of the immersed finite element method to a high-order immersed finite element method for solving one-dimensional parabolic interface problems. In addition, we introduce a nonconforming immersed finite element method to solve the two-dimensional parabolic problem with a moving interface. In the nonconforming IFE framework, the degrees of freedom are determined by the average integral value over the element edges. The continuity of the nonconforming IFE framework is in the weak sense in comparison the continuity of the conforming IFE framework. Numerical experiments are provided to demonstrate the features and the robustness of these methods. We introduce a class of lowest-order nonconforming immersed finite element methods for solving two-dimensional Stokes interface problem. On triangular meshes, the Crouzeix-Raviart element is used for velocity approximation, and piecewise constant for pressure. On rectangular meshes, the Rannacher-Turek rotated $Q_1$-$Q_0$ finite element is used. We also consider a new mixed immersed finite element method for the Stokes interface problem on an unfitted mesh. The proposed IFE space uses conforming linear elements for one velocity component and nonconforming linear elements for the other component. The new vector-valued IFE functions are constructed to approximate the interface jump conditions. Basic properties including the unisolvency and the partition of unity of these new IFE methods are discussed. Numerical approximations are observed to converge optimally. Lastly, we apply each class of the new immersed finite element methods to solve the unsteady Stokes interface problem. Based on the new IFE spaces, semi-discrete and full-discrete schemes are developed for solving the unsteady Stokes equations with a stationary or a moving interface. A comparison of the degrees of freedom and number of elements are presented for each method. Numerical experiments are provided to demonstrate the features of these methods.

Master of Science / Department of Mechanical and Nuclear Engineering / Steve Eckels / A new three dimensional transient human finger model was developed to predict the risk of frostbite in humans at different environmental conditions. The shape of the finger model was similar to that of a real human finger. Finite Element Techniques were used to build the finger model. Smith’s Model (1991) energy balance equations were used to calculate the temperatures in the current finger model. The current 3D finger model was validated against the experimental data of Wilson (1976) and Santee (1990). The model agreed well with the Wilson experiments and with the cold test in Santee experiments. The comparison indicates that the current finger model can be used to adequately predict the human finger responses in different environments. The current finger model was then tested in temperatures of 0, -10, -20, -25 and -30 oC and with different airspeeds 0, 3 and 6.8 m/s to assess the risk of frostbite in humans. Three resistances 0, 0.4 and 0.8 clo were used on the finger model to obtain responses in different environmental conditions. From the experimental results, an expression for safe glove resistance required to prevent frostbite in known temperatures was calculated. Also, the temperatures up to which a glove with known thermal resistance value can protect a human finger from frostbite was also computed.

In this scientific work, we use two effective methods : Lie groups theory and the finite element method, to explain why the transition from laminar flow to turbulence flow depends on the variation of the Reynolds number. We restrict ourselves to the case of incompressible viscous Newtonian fluid flows. Their governing equations, i.e. the continuity and Navier-Stokes equations are established and investigated. Their solutions are expressed explicitly thanks to Lie's theory. The stability theory, which leads to an eigenvalue problem is used together with the finite element method, showing a way to compute the critical Reynolds number, for which the transition to turbulence occurs. The stationary flow is also studied and a finite element method, the Newton method, is used to prove the stability of its convergence, which is guaranteed for small variations of the Reynolds number. / Mathematical Sciences / M.Sc. (Applied Mathematics)

It is of great clinical importance to predict the behaviour of the cornea in various diseases and post-surgical recovery. Therefore, a numerical model that is able to simulate the corneal behaviour, considering corneal material properties obtained from individuals is highly desirable. In this work a combined numerical-experimental technique has been developed that can characterize the mechanical properties of a cornea properties from two aspects: time-dependency and spatial variation. Initially, an analysis of the material properties of porcine corneas was performed to investigate the time-dependent behaviour of the cornea. A simple stress relaxation test was used to determine the viscoelastic properties of a cornea and a rheological model was built based on the Generalized Maxwell (GM) approach. A validation experiment using nano-indentation showed that an isotropic GM model was insufficient for describing the corneal time-dependent behaviour when exposed to a complex stress state. A technique was proposed that takes into account the microstructural composition of the cornea and is based on a combination of nano-indentation experiment, isotropic and transversely isotropic numerical models, and an inverse finite element method. The good agreement using this method suggests that this is a promising technique for measuring the time-dependent properties of the cornea. The spatial variation of the properties was then investigated. This time, the long term structural response of the cornea was targeted. A full field displacement response of a loaded cornea was evaluated from Optical Coherence Tomography (OCT) volume reconstructions of the cornea using Digital Volume Correlation (DVC). The inverse finite element method was employed with two models sequentially; first, a radially partitioned model and then a circumferentially partitioned model, in order to recover the elastic parameters in radial and circumferential directions. The good agreement using this method suggests that this is a promising and reliable technique for identifying the distribution of the corneal properties. In this research, we have shown that it is possible to determine the local time-dependent properties of the cornea and the in-depth (2D) distribution of the properties using the hybrid technique. This technique has the potential to be implemented in vivo. However, further work should focus on the feasibility of this technique in practice.