Why this matters
Most everyday design tools treat trusses as linear, even though real structures can show large deflections, snap-through, and catenary action under extreme loads. This project was about building my own nonlinear analysis and optimization framework so I could actually see and quantify those behaviors, rather than relying on black-box commercial software.
What I built
Starting from a basic 2D truss code, I extended it into a geometric nonlinear matrix analysis program in MATLAB. Using the direct stiffness method with an additional geometric stiffness term, the solver can perform second-order elastic analysis of pin-jointed trusses. I implemented both load-controlled and arc-length procedures to trace the full load–displacement response, including unstable branches and snap-through in benchmark problems like a shallow three-hinged arch and a truss-arch bridge.
Optimization and insights
On top of the analysis engine, I coded a structural optimization module that redistributes member areas to either minimize weight under a displacement constraint, or minimize displacement for a fixed weight. The algorithm uses virtual work and an optimality criterion based on equalizing strain energy per unit volume, and can automatically remove redundant members. Applied to the arch bridge, it reproduced reference results from MASTAN2 while identifying a lighter design that still met displacement targets. The project gave me a ground-up understanding of nonlinear truss behavior, numerical solution methods, and physically meaningful optimization criteria.