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Structural Optimization

Structural optimization deals with the optimal design of load-carrying mechanical structures. Basically a structural optimization is referd to as topology optimization, where a typical problem may be a given predefined design domain, some given supports in connection to the design domain, some given external loads, and a given material to be used, the problem consists of designing an optimal structure to carry the given loads, etc. All these problems can be solved done by finding the optimal subdomain, of the given design domain, to fill with material. The objective of structural optimization is to minimize the total weight of the structure subject to constraints on displacements and stresses in the structure under the given loads. This problem can also be solved numerically as the design domain is discretized by a finite element model. For this a discretized universe in which for each individual there is a discrete point, i.e. finite element, which decides where to place that material.

Structural optimization or the numerical optimization techniques are used to design a structure which is material-efficient and cost-effective and this has great potential for the construction industry. Structural optimization helps to reduce construction industry cost , so improving the sustainability of the sector. Structural optimization also has the potential to reduce not only the construction cost, but also the engineering cost, by automating the repetitive task of sizing structural members. And the structural optimization can lead to innovative design solutions for a specific structural components or materials.

Size Optimization, Shape Optimization, Topology Optimization, Buildability, Robust and Reliability-Based Design Optimization are some of the important keywords of structural optimization.

Few Topics are:

  • Structural Synthesis
  • Elasticity & Axial Bar
  • Finite Element Stiffness of Axial Bar
  • Finite Element Assembly of Trusses
  • Calculus
  • Method of Lagrange Multipliers
  • Karush-Kuhn-Tucker Optimality Conditions
  • Sensitivity Analysis of Discrete Systems
  • Direct Method for Sensitivity Derivatives
  • Adjoint Method for Sensitivity Derivatives
  • Sensitivity of Natural Frequencies
  • Complex Step Derivatives
  • Linear Programming
  • Simplex Algorithm
  • Sequential Linear Programming
  • Numerical Optimization
  • Fully Stressed Design
  • Optimality Criterion Methods
  • Topology Optimization
  • Solid Isotropic Material
  • Sequential Quadratic Programming
  • Approximation Concepts
  • Reciprocal Approximation
  • Force Approximation
  • Rayleigh Quotient Approximation
  • Dual Formulation
  • Conservative Approximation
  • Method of Moving Asymptotes
  • Two-Point Exponential Approximation
  • Move Limits & Constraint Deletion
  • Trust Regions
  • Shape Optimization
  • Multi-Objective Optimization
  • Genetic Algorithms
  • Discrete Variables