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.
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.
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.