Mechanical Engineering
 

(Me En-CE En) Computer Structural Analysis and Optimization

(Me En-CE En) Computer Structural Analysis and Optimization
Matrix stiffness method for 1D, 2D, and 3D skeletal structure classes. Implementing the matrix stiffness method as a computer program. Nonlinear second-order structural analysis. Structural optimization techniques including stress-ratio method, gradient-based methods, and genetic algorithms.
ME EN
504
 Hours3.0 Credit, 3.0 Lecture, 0.0 Lab
 PrerequisitesME EN 372 & MATH 302; or ME EN 372 & MATH 313; or CE EN 321 & MATH 313
 TaughtFall
Course Outcomes: 

Member Stiffness and Force

Construct global and local member stiffness matrices and force vectors for any skeletal class and any distributed loading.

Structure Stiffness and Force

Construct structure matrices and vectors for both force and support displacement loads exploiting symmetry/antisymmetry and deformation assumptions.

Member Results

Construct member displacement vectors and free-body diagrams for any skeletal class.

Analysis Program Organization

Write down the basic organization and calling structure of a structural analysis program, and complete the pseudo-code for structure level routines.

Second Order Analysis

Derive first/second order equilibrium/compatibility equations, buckling loads/displacements, and structure elastic/geometric stiffness matrices for small trusses and single-member frames.

Matrix Vector Operations

Determine the number of FLOPS and perform the calculations for matrix-vector operations including triangularization, backsubstitution, Newton-Raphson iteration, and inverse iteration.

Stress Ratio and Exhaustive Search

Determine the number of FLOPS and perform the calculations for stress ratio optimization and exhaustive search, and construct design space plots if possible.

Optimality Criteria Algorithms

Determine the number of FLOPS and perform the calculations for finite difference / virtual work sensitivity analysis, Kuhn-Tucker condition evaluation, and optimality criteria algorithm.

Genetic Algorithms

Determine the number of FLOPS and perform the calculations for genetic algorithms with penalty/segregation fitness, tournament/roulette selection, point/uniform/blend crossover, dynamic mutation, and ranking/scoring/maximin fitness.

Execute Structural Software

Prepare input for linear analysis, nonlinear pushover analysis, gradient-based size optimization, and genetic-based size/shape/topology optimization programs for plane frames.