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

(CE En-Me 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.
CE EN
504
 Hours 3.0 Credit, 3.0 Lecture, 0.0 Lab Prerequisites CE EN 321; or ME EN 372; or equivalent; linear algebra. Taught Programs Containing CE EN 504
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.