Gary F. Dargush

Boundary element method for dynamic poroelastic and thermoelastic analyses

Abstract A boundary element method is developed for transient and time harmonic analysis of problems in dynamic poroelasticity and generalized thermoelasticity, involving both two- and three-dimensional geometries. Laplace domain infinite space fundamental solutions are employed to produce a formulation that requires only surface discretization. Consequently, the resulting algorithm provides an attractive alternative to existing volume-based methods, particularly for media of infinite extent. Details of the formulation and numerical implementation are presented. Several applications are included to validate the method and to emphasize certain aspects of the dynamic theory.

Computer modeling of deployment and mechanical expansion of neurovascular flow diverter in patient-specific intracranial aneurysms

Flow diverter (FD) is an emerging neurovascular device based on self-expandable braided stent for treating intracranial aneurysms. Variability in FD outcome has underscored a need for investigating the hemodynamic effect of fully deployed FD in patient-specific aneurysms. Image-based computational fluid dynamics, which can provide important hemodynamic insight, requires accurate representation of FD in deployed states. We developed a finite element analysis (FEA) based workflow for simulating mechanical deployment of FD in patient-specific aneurysms. We constructed FD models of interlaced wires emulating the Pipeline Embolization Device, using 3D finite beam elements to account for interactions between stent strands, and between the stent and other components. The FEA analysis encompasses all steps that affect the final deployed configuration including stent crimping, delivery and expansion. Besides the stent, modeling also includes key components of the FD delivery system such as microcatheter, pusher, and distal coil. Coordinated maneuver of these components allowed the workflow to mimic clinical operation of FD deployment and to explore clinical strategies. The workflow was applied to two patient-specific aneurysms. Parametric study indicated consistency of the deployment result against different friction conditions, but excessive intra-stent friction should be avoided. This study demonstrates for the first time mechanical modeling of braided FD stent deployment in cerebral vasculature to produce realistic deployed configuration, thus paving the way for accurate CFD analysis of flow diverters for reliable prediction and optimization of treatment outcome.

Multi-Objective Evolutionary Seismic Design with Passive Energy Dissipation Systems

The problem of multi-objective seismic design optimization is examined within the context of passive energy dissipation systems. In particular, a genetic algorithm approach is developed to enable the evaluation of the Pareto front, where maximum inter-story drifts and maximum total accelerations, both important measures for damage, serve as objectives. Here the cost of the passive system is considered as a constraint, although it could be included instead as a third objective. Hysteretic, viscoelastic and viscous dampers are all considered as possible design strategies, as well as the weakening plus damping concept. Since different types of passive systems are included, diversity of the Pareto front becomes a key issue, which is addressed successfully through an innovative definition of fitness. The multi-objective framework enables the evaluation of trade-offs between the two objectives and, consequently, provides vital information for the decision maker. Furthermore, the results presented offer valuable insight into the characteristics of optimal passive designs for the different objectives. Some of these characteristics confirm results reported elsewhere, while others are presented here for the first time.

A poly-region boundary element method for incompressible viscous fluid flows

A boundary element method (BEM) for steady viscous fluid flow at high Reynolds numbers is presented. The new integral formulation with a poly-region approach involves the use of the convective kernel with slight compressibility that was previously employed by Grigoriev and Fafurin [1] for driven cavity flows with Reynolds numbers up to 1000. In order to avoid the overdeterminancy of the global set of equations when using eight-noded rectangular volume cells from that previous work, 12-noded hexagonal volume regions are introduced. As a result, the number of linearly independent integral equations for each node becomes equal to the degrees of freedom of the node. The numerical results for square-driven cavity flow having Reynolds numbers up to 5000 are compared to those obtained by Ghia et al. [2] and demonstrate a high level of accuracy even in resolving the secondary vortices at the corners of the cavity. Next, a comprehensive study is done for backward-facing step flows at Re=500 and 800 using the BEM, along with a standard Galerkin-based finite element methods (FEM). The numerical methods are in excellent agreement with the benchmark solution published by Gartling [3]. However, several additional aspects of the problem are also considered, including the effect of the inflow boundary location and the traction singularity at the step corner. Furthermore, a preliminary comparative study of the poly-region BEM versus the standard FEM indicates that the new method is more than competitive in terms of accuracy and efficiency. Copyright

Development of a boundary element method for time-dependent planar thermoelasticity

Abstract A new boundary element method is developed for two-dimensional quasistatic thermoelasticity. This time domain formulation involves only surface quantities. Consequently, volume discretization is completely eliminated and the method becomes a viable alternative to the usual finite element approaches. After presenting a brief overview of the governing equations, boundary integral equations for coupled quasistatic thermoelasticity are derived by starting with existing fundamental solutions along with an appropriate reciprocal theorem. Details of a general purpose numerical implementation are then discussed. Next. boundary element methods for the two more practical theories, uncoupled quasistatic and steady-state thermoelasticity, are developed directly from limiting forms of the coupled formulation. Several numerical examples are provided to illustrate the validity and attractiveness of the boundary element approach for this entire class of problems.

Thermal expansion of the workpiece in turning

Thermal expansion of the part can be a significant source of dimensional and form errors in precision machining operations. This paper describes a method for calculating the thermal expansion of an axisymmetric workpiece. The analysis is based on a commercially available boundary element code modified to properly represent concentrated moving heat sources such as those produced in machining. The inputs required are the amount of heat entering the part from the cutting zone and the thermal properties of the workpiece material. Calculations are compared with direct measurements of expansion from tests on large diameter 2024 aluminum sleeves. The agreement between calculated and measured values is generally reasonable, although calculated expansions are consistently smaller than measured expansions. This error is probably due to errors in estimating the heat input to the part, and particularly the neglect of flank friction in heat input calculations. Sample calculations for hard turning of a wheel spindle show that expansions can approach tolerances on critical surfaces. Based on sample calculations, thermal expansion is likely to be significant when hard turning parts with tolerances on the order of 0.01 mm. For these applications, critical surfaces should be machined first, before cuts on other sections heat the part, and gaging should be carried out only after the part has cooled.

Boundary element methods in three-dimensional thermoelasticity

Abstract A boundary element method is developed for the solution of time-dependent problems in three-dimensional thermoelasticity. The time domain, boundary-only formulation represents the first of its kind for quasistatic analysis, which by definition considers transient heat conduction, but ignores the effects of inertia. By eliminating the need for volume discretization, the method becomes an attractive alternative to finite element analysis for this class of problems. Additionally, because an exact Greens function is used in the interior, steep thermal gradients can be captured much more readily than with standard domain-based methods. The presentation includes details of the fundamental solution, a derivation of the boundary integral equations, and an overview of a general purpose numerical implementation. This implementation permits the solution of large, multiregion problems with arbitrary geometry and boundary conditions. Several examples are included to validate the proposed method, as well as to highlight its usefulness.

A boundary element method for axisymmetric soil consolidation

Abstract The development of a time domain boundary element method for axisymmetric quasistatic poroelasticity is discussed. This new formulation, for the complete Biot consolidation theory, has the distinct advantage of being written exclusively in terms of boundary variables. Thus, no volume discretization is required, and the approach is ideally suited for geotechnicul problems involving media of infinite extent. In the presentation, the required axisymmetric integral equations and kernel functions are first developed from the corresponding three-dimensional theory. In particular, emphasis is placed on the analytical and numerical treatment of the kernels. This is followed by an overview of the numerical implementation, and a demonstration of its merits via the consideration of several examples.

Mixed Lagrangian Formulation for Linear Thermoelastic Response of Structures

AbstractAlthough a complete unified theory for elasticity, plasticity, and damage does not yet exist, an approach on the basis of thermomechanical principles may be able to serve as the foundation for such a theory. With this in mind, as a first step, a mixed formulation is developed for fully coupled, spatially discretized linear thermoelasticity under the Lagrangian formalism by using Hamilton’s principle. A variational integration scheme is then proposed for the temporal discretization of the resulting Euler-Lagrange equations. With this discrete numerical time-step solution, it becomes possible, for proper choices of state variables, to restate the problem in the form of an optimization. Ultimately, this allows the formulation of a principle of minimum generalized complementary potential energy for the discrete-time thermoelastic system.

Theory of Boundary Eigensolutions in Engineering Mechanics

A theory of boundary eigensolutions is presented for boundary value problems in engineering mechanics. While the theory is quite general, the presentation here is restricted to potential problems. Contrary to the traditional approach, the eigenproblem is formed by inserting the eigenparameter, along with a positive weight function, into the boundary condition. The resulting spectra are real and the eigenfunctions are mutually orthogonal on the boundary, thus providing a basis for solutions. The weight function permits effective treatment of nonsmooth problems associated with cracks, notches and mixed boundary conditions. Several ideas related to the convergence characteristics are also introduced. Furthermore, the connection is made to integral equation methods and variational methods. This paves the way toward the development of new computational formulations for finite element and boundary element methods. Two numerical examples are included to illustrate the applicability.