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Truss Topology Using Liner Programming

Truss topology.jpg

What?

  • Designed an efficient truss system by selecting optimal members from 24090 possible elements in an 11x20 grid using linear programming (LP).
  • Two Optimization Goals:
    •  Minimize internal forces to reduce material usage
    • Minimize length and internal forces for a lightweight, efficient structure.
  • Applied MATLAB's linprog() function to solve for equilibrium forces while adhering to material constraints.

How?

  • Problem Simplification: Reduced complexity by analyzing a smaller 2x4 truss system, identifying patterns before scaling up to the full 11x20 grid.
  • Used force balance equations and defined equality (Aeq, beq) and inequality (Aineq, bineq) constraints based on internal forces and material yield strength.
  • Cost Function Optimization:
    • Method 1: Minimized total internal forces using the L1 norm.​
    • Method 2: Minimized both length and internal forces, incorporating element lengths from Pythagorean calculations.

Result

  • Optimized Truss Design:
    • Force-only optimization: 14 truss members selected for minimal internal force distribution.​
    • Length and force optimization: 189 truss members selected, forming a teardrop-like structure concentrated near anchor points.
  • Methodology can be applied to larger truss optimization problems, improving real-world structural designs.
  • Click Here to see the detailed report.

Project Images

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