Monte Carlo Simulations of Coupled Transient Seepage Flow and Soil Deformation in Levees

The purpose of this research is to compare the results from two different computer programs of flow analysesof two levees at Port Arthur, Texas where rising water of a flood from Hurricane Ike occurred on the levees. The first program (Program 1) is a two-dimensional (2-D) transient finite element program that couples the conservation of mass flow equation with accompanying hydraulic boundary conditions with the conservation of force equations with accompanying x and y displacement and force boundary conditions, thus yielding total head, x displacement, and y displacement as unknowns at each finite element node. The second program (Program 2) is a 2-D transient finite element program that considers only the conservation of mass flowequation with its accompanying hydraulic boundary conditions, yielding only total head as the unknown at each finite element node. Compressive stresses can be computed at the centroid of each finite element when using the coupled program. Programs 1 and 2 were parallelized for high performance computing to consider thousands of realisations of the material properties. Since a single realisation requires as much as one hour of computer time for certain levees, the large realisation computation is made possible by utilising HPC. This Monte Carlo type analysis was used to compute the probability of unsatisfactory performance for under seepage, through seepage, and uplift for the two levees. Respective hydrographs from the flood resulting from Hurricane Ike were applied to each levee. When comparing the computations from the two programs, the most significant result was the two programs yielded significantly different values in the computed results in the two clay levees considered in this research.

Numerical Modelling of Boundary Layers and Far Field Acoustic Propagation in Thermoviscous Fluid

To model linear acoustics in a thermoviscous fluid in open domain and time-harmonic regime, a Finite Element formulation in a bounded meshed domain is combined with the integral representation of the field for the propagative solution. The integrals are non-singular and involve the only Finite Element node values for temperature variation and particle velocity variables. To overcome the non-uniqueness of solutions at fictitious resonant frequencies, a Burton-Miller combination of integral representation is used. This formulation is suitable to compute acoustic radiation, scattering and diffraction by objects or mutual interaction between transducers. Two-dimensional computational experiments are presented in an infinite, open domain (exterior), showing that the model can be achieved in meshing only a thin domain surrounding the physical boundaries of a device.

Distributing Three-Dimensional Aerodynamic Load to Fem Nodes

Aiming at the requirement of the load conversion in aeronautics and astronautics static strength analysis, a three-dimensional aerodynamic load equivalent distribution method based on least squares is proposed. Based on the principle of the closest distance, the corresponding relationship between the aerodynamic node and the finite element node is established to ensure that each finite element node has its corresponding aerodynamic node. Under the requirement of minimizing the variance of load obtained by each node allocation, the least squares algorithm is used to obtain the results of the load conversion. Through an engineering example of aerodynamic distribution, it is verified that the method presented in this paper not only has high accuracy but also can ensure the uniformity of load distribution before and after load distribution.

Node-dependent kinematic elements for the dynamic analysis of beams with piezo-patches

This article extends the use of one-dimensional elements with node-dependent kinematics to the dynamic analysis of beam structures with piezo-patches. Node-dependent kinematics allows the kinematic assumptions to be defined individually on each finite element node, leading to finite element models with variable nodal kinematics. Derived from Carrera unified formulation, node-dependent kinematics facilitates the mathematical refinement to an arbitrary order at any desirable region on the nodal level while keeping the compactness of the formulation. As an ideal approach to simulate structures with special local features, node-dependent kinematics has been employed to model piezo-patches in static cases. In this work, the application of node-dependent beam elements in dynamic problems is demonstrated. Node-dependent kinematics is applied to increase the numerical accuracy in the areas where the piezo-patches lie in through sufficiently refined models, while lower order assumptions are used elsewhere. The dissimilar constitutive relations of neighboring components are appropriately considered with layer-wise models. Both open- and short-circuit conditions are considered. The results are compared against those from literature. The numerical study shows that the adoption of node-dependent kinematics allows accurate results to be obtained at reduced computational costs.

Quench Process Modeling and Optimization

We optimize continuous quench process parameters to produce a desired precipitate distribution in aluminum alloy extrudates. To perform this task, an optimization problem is defined and solved using a standard nonlinear programming algorithm. Ingredients of this algorithm include a cost function, constraint functions and their sensitivities with respect to the process parameters. These functions are dependent on the temperature and precipitate size which are obtained by balancing energy to determine the temperature distribution and by using a reaction-rate theory to determine a discrete precipitate particle size distribution. Both the temperature and the precipitate models are solved via the finite element method. Since we use a discrete particle size model, there are as many as 105 degrees-of-freedom per finite element node. After we compute the temperature and precipitate size distributions, we must also compute their sensitivities. This seemingly intractable computational task is resolved by using an element-by-element discontinuous Galerkin finite element formulation and a direct differentiation sensitivity analysis which allows us to perform all of the computations on a PC.

Dynamic Modeling of a Flexible Manipulator With Prismatic Links

In this paper the equations of motion for a flexible multi-link manipulator are derived. Each link of the manipulator, including those with prismatic motion, is represented by two finite elements in three-dimensional space. The prismatic links are treated as beams with moving boundary conditions, and the position of finite-element node points are not changed relative to the link. The equations are generated using Maple V, and the paper discusses a general approach for eliminating small terms. A sample calculation is performed for a RRP (Stanford arm) manipulator, and the shift of natural frequencies with time are plotted. Results are compared to those obtained by the assumed-mode method.

Effective constitutive algorithms in elastoplasticity and elastoviscoplasticity

The basic constitutive relations for elastoplasticity and elastoviscoplasticity are shown to form a typical boundary layer-type stiff system of ordinary differential equations. Three numerical algorithms are discussed: (i) The singular perturbation method (O'Malley, 1971a, b; Hoppensteadt, 1971; Miranker, 1981; Smith, 1985), which yields accurate results for both the rate-independent and rate-dependent cases, where in the former case, the algorithm is explicit, whereas in the latter case, it is implicit and requires the solution of a nonlinear equation; therefore it is impractical as a constitutive algorithm for large-scale finite-element applications, where the constitutive algorithm is used a great number of times at each finite-element node. (ii) The new constitutive algorithm (Nemat-Nasser, 1991; Nemat-Nasser & Chung, 1989, 1992) which is explicit and accurate for both the rate-independent and rate-dependent cases; the underlying mathematical feature of this new method is investigated, and it is shown that it can be classified as a simplified perturbation method; computable error bounds for this algorithm are obtained, and when the flow rule is given by the commonly used power law, it is shown that the errors are very small, (iii) A modified outer-solution method, which combines the above two techniques, and is simple, explicit, and accurate.

An Algorithm for Two-Dimensional Geometric Boundary Construction From Finite Element Node Displacement Data

This paper describes a system for constructing geometric models from elastically deflected finite element meshes. Two dimensional boundary curves are constructed by fitting B-Spline curves to the deflected Finite Element model. Cubic B-Splines are generated using least squares fitting techniques to the boundary curves of the Finite Element results. The fitted curves are connected end-to-end. The algorithm is useful after analysis for interfacing analysis results with design data in a shape optimization system based on Finite Element techniques.