printer friendly pageME 333B: Mechanics - Elasticity and Inelasticity
Introduction to the theories of elasticity, plasticity and fracture and their applications. Elasticity: Definition of stress, strain, and elastic energy; equilibrium and compatibility conditions; and formulation of boundary value problems. Stress function approach to solve 2D elasticity problems and Greenâs function approach in 3D. Applications to contact and crack. Plasticity: Yield surface, associative flow rule, strain hardening models, crystal plasticity models. Applications to plastic bending, torsion and pressure vessels. Fracture: Linear elastic fracture mechanics, J-integral, Dugdale-Barrenblatt crack model. Applications to brittle fracture and fatigue crack growth. Computer programming in Matlab is used to aid analytic derivation and numerical solutions.
Terms: Win
| Units: 3
Instructors:
Cai, W. (PI)
;
Akhondzadeh, H. (TA)
ME 333C: Mechanics - Continuum Mechanics
Introduction to linear and nonlinear continuum mechanics of solids. Introduction to tensor algebra and tensor analysis. Kinematics of motion. Balance equations of mass, linear and angular momentum, energy, and entropy. Constitutive equations of isotropic and anisotropic hyperelastic solids. Introduction to numerical solution techniques.
Terms: Spr
| Units: 3
ME 335A: Finite Element Analysis
Fundamental concepts and techniques of primal finite element methods. Method of weighted residuals, Galerkin's method and variational equations. Linear eliptic boundary value problems in one, two and three space dimensions; applications in structural, solid and fluid mechanics and heat transfer. Properties of standard element families and numerically integrated elements. Implementation of the finite element method using Matlab, assembly of equations, and element routines. Lagrange multiplier and penalty methods for treatment of constraints. The mathematical theory of finite elements.
Terms: Aut
| Units: 3
Instructors:
Pinsky, P. (PI)
;
Hwang, Y. (TA)
ME 335B: Finite Element Analysis
Finite element methods for linear dynamic analysis. Eigenvalue, parabolic, and hyperbolic problems. Mathematical properties of semi-discrete (t-continuous) Galerkin approximations. Modal decomposition and direct spectral truncation techniques. Stability, consistency, convergence, and accuracy of ordinary differential equation solvers. Asymptotic stability, over-shoot, and conservation laws for discrete algorithms. Mass reduction. Applications in heat conduction, structural vibrations, and elastic wave propagation. Computer implementation of finite element methods in linear dynamics. Implicit, explicit, and implicit-explicit algorithms and code architectures.
Terms: Win
| Units: 3
Instructors:
Pinsky, P. (PI)
;
Hwang, Y. (TA)
ME 335C: Finite Element Analysis
Newton's method for nonlinear problems; convergence, limit points and bifurcation; consistent linearization of nonlinear variational forms by directional derivative; tangent operator and residual vector; variational formulation and finite element discretization of nonlinear boundary value problems (e.g. nonlinear heat equation, nonlinear elasticity); enhancements of Newton's method: line-search techniques, quasi-Newton and arc-length methods.
Terms: Sum
| Units: 3
Instructors:
Pinsky, P. (PI)
;
Sahli, F. (TA)
ME 337: Mechanics of Growth
Introduction to continuum theory and computational simulation of living matter. Kinematics of finite growth. Balance equations in open system thermodynamics. Constitutive equations for living systems. Custom-designed finite element solution strategies. Analytical solutions for simple model problems. Numerical solutions for clinically relevant problems such as: bone remodeling; wound healing; tumor growth; atherosclerosis; heart failure; tissue expansion; and high performance training.
Last offered: Winter 2015
ME 338: Continuum Mechanics
Linear and nonlinear continuum mechanics for solids. Introduction to tensor algebra and tensor analysis. Kinematics of motion. Balance equations of mass, linear and angular momentum, energy, and entropy. Constitutive equations of isotropic and anisotropic hyperelasticity. Recommended as prerequisite for Finite Element Methods.
Terms: Sum
| Units: 3
Instructors:
Lew, A. (PI)
;
Kim, K. (TA)
ME 338B: Continuum Mechanics
Constitutive theory; equilibrium constitutive relations; material frame indifference and material symmetry; finite elasticity; formulation of the boundary value problem; linearization and well-posedness; symmetries and configurational forces; numerical considerations.
Last offered: Spring 2007
ME 339: Introduction to parallel computing using MPI, openMP, and CUDA (CME 213)
This class will give hands on experience with programming multicore processors, graphics processing units (GPU), and parallel computers. Focus will be on the message passing interface (MPI, parallel clusters) and the compute unified device architecture (CUDA, GPU). Topics will include: network topologies, modeling communication times, collective communication operations, parallel efficiency, MPI, dense linear algebra using MPI. Symmetric multiprocessing (SMP), pthreads, openMP. CUDA, combining MPI and CUDA, dense linear algebra using CUDA, sort, reduce and scan using CUDA. Pre-requisites include: C programming language and numerical algorithms (solution of differential equations, linear algebra, Fourier transforms).
Terms: Spr
| Units: 3
ME 340: Theory and Applications of Elasticity
This course provides an introduction to the elasticity theory and its application to material structures at microscale. The basic theory includes the definition of stress, strain and elastic energy; equilibrium and compatibility conditions; and the formulation of boundary value problems. We will mainly discuss the stress function method to solve 2D problems and will briefly discuss the Green's function approach for 3D problems. The theory and solution methods are then applied to contact problems as well as microscopic defects in solids, such as voids, inclusions, cracks, and dislocations. Computer programming in Matlab is used to aid analytic derivation and numerical solutions of elasticity problems.
Last offered: Winter 2013
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