arXiv subjects

Kurt Maute

Publications and source records attributed to Kurt Maute.

22 records · Page 2Linked to original sources

arXiv2017

Level set shape and topology optimization of finite strain bilateral contact problems

This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit level set method, which allows for both shape and topology changes. The mechanical model assumes finite strains, a nonlinear elastic material behavior, and a quasi-static response. Identification of overlapping surface position is handled by a coupled parametric representation of contact surfaces. A stabilized Lagrange method and an active set strategy are used to model frictionless contact and separation. The mechanical model is discretized by the extended finite element method which maintains a clear definition of geometry. Face-oriented ghost penalization and dynamic relaxation are implemented to improve the stability of the physical response prediction. A nonlinear programming scheme is used to solve the optimization problem, which is regularized by introducing a perimeter penalty into the objective function. Sensitivities are determined by the adjoint method. The main characteristics of the proposed method are studied by numerical examples in two dimensions. The numerical results demonstrate improved design performance when compared to models optimized with a small strain assumption. Additionally, examples with load path dependent objectives display non-intuitive designs.

math.OC↗

arXiv2015

On Uncertainty Quantification of Lithium-ion Batteries: Application to an LiC$_6$/LiCoO$_2$ cell

In this work, a stochastic, physics-based model for Lithium-ion batteries (LIBs) is presented in order to study the effects of parametric model uncertainties on the cell capacity, voltage, and concentrations. To this end, the proposed uncertainty quantification (UQ) approach, based on sparse polynomial chaos expansions, relies on a small number of battery simulations. Within this UQ framework, the identification of most important uncertainty sources is achieved by performing a global sensitivity analysis via computing the so-called Sobol' indices. Such information aids in designing more efficient and targeted quality control procedures, which consequently may result in reducing the LIB production cost. An LiC$_6$/LiCoO$_2$ cell with 19 uncertain parameters discharged at 0.25C, 1C and 4C rates is considered to study the performance and accuracy of the proposed UQ approach. The results suggest that, for the considered cell, the battery discharge rate is a key factor affecting not only the performance variability of the cell, but also the determination of most important random inputs.

physics.comp-ph↗

arXiv2014

Density and Level Set-XFEM Schemes for Topology Optimization of 3-D Structures

As the capabilities of additive manufacturing techniques increase, topology optimization provides a promising approach to design geometrically sophisticated structures which can be directly manufactured. Traditional topology optimization methods aim at finding the conceptual design but often lack a sufficient resolution of the geometry and structural response, needed to directly use the optimized design for manufacturing. To overcome these limitations, this paper studies the viability and characteristics of the eXtended Finite Element Method (XFEM) in combination with the Level-Set Method (LSM) for topology optimization of three dimensional structural design problems. The LSM describes the geometry by defining the nodal level set values via explicit functions of the optimization variables. The structural response is predicted by a generalized version of the XFEM. The LSM-XFEM approach is compared against results from a traditional Solid Isotropic Material with Penalization (SIMP) method for two-phase ``solid-void'' and ``solid-solid'' problems. The numerical results demonstrate that the LSM-XFEM approach can describe crisply the geometry and predict the structural response of complex three-dimensional structures with acceptable accuracy even on coarse meshes. However, the LSM-XFEM studied here lacks a robust and intuitive formulation to control the minimum feature size, and the optimization results may depend on the initial design.

math.OC↗

arXiv2013

A Simple and Efficient Preconditioning Scheme for Heaviside Enriched XFEM

The eXtended Finite Element Method (XFEM) is an approach for solving problems with non-smooth solutions. In the XFEM, the approximate solution is locally enriched to capture discontinuities without requiring a mesh which conforms to the geometric features. One drawback of the XFEM is that an ill-conditioned system of equations results when the ratio of volumes on either side of the interface in an element is small. In this paper, to avoid this ill-conditioning, a simple and efficient scheme based on a geometric preconditioner and constraining degrees of freedom to zero for small intersections is proposed. This geometric preconditioner is computed from the nodal basis functions, and therefore may be constructed prior to building the system of equations. This feature and the low-cost of constructing the preconditioning matrix makes it well suited for nonlinear problems with fixed and moving interfaces.

math.NA↗