ST4012 Optimization of Structures Syllabus:
ST4012 Optimization of Structures Syllabus – Anna University PG Syllabus Regulation 2021
OBJECTIVE:
To study the optimization methodologies applied to structural engineering
UNIT I BASIC PRINCIPLES AND CLASSICAL OPTIMIZATION TECHNIQUES
Definition – Objective Function; Constraints – Equality and inequality – Linear and non-linear Side, Non-negativity, Behaviour and other constraints – Design space – Feasible and infeasible- Convex and Concave – Active constraint – Local and global optima. Differential calculus – Optimality criteria – Single variable optimization – Multivariable optimization with no constraints- – (Lagrange Multiplier method) – with inequality constraints (Khun – Tucker Criteria).
UNIT II LINEAR AND NON-LINEAR PROGRAMMING
LINEAR PROGRAMMING: Formulation of problems -Graphical solution – Analytical methods- Standard form – Slack, surplus and artificial variables – Canonical form – Basic feasible solution – simplex method – Two phase method – Penalty method- Duality theory – Primal – Dual algorithm, Dual Simplex method. Non-linear programming: One Dimensional minimization methods: Unidimensional – Unimodal function – Exhaustive and unrestricted search – Dichotomous search – Fibonacci Method – Golden section method -Interpolation methods. Unconstrained optimization Techniques.
UNIT III GEOMETRIC PROGRAMMING
Polynomial – degree of difficulty – reducing G.P.P to a set of simultaneous equations – Unconstrained and constrained problems with zero difficulty – Concept of solving problems with one degree of difficulty.
UNIT IV DYNAMIC PROGRAMMING
Bellman’s principle of optimality – Representation of a multistage decision problem- concept of sub-optimization problems using classical and tabular methods.
UNIT V STRUCTURAL APPLICATIONS
Methods for optimal design of structural elements, continuous beams and single storied frames using plastic theory -Minimum weight design for truss members – Fully stressed design – Optimization principles to design of R.C. structures such as multistory buildings, water tanks and bridges.
OUTCOMES:
On completion of the course, the student is expected to be able to
CO1 Apply the knowledge of engineering fundamentals to formulate and solve engineering problems by classical optimization techniques.
CO2 Identify, formulate and solve engineering problems by linear and non-linear programming.
CO3 Analyse the problem and reduce G.P.P to a set of simultaneous equations.
CO4 Apply the Engineering knowledge to understand the concept of dynamic programming.
CO5 Design various structural elements with minimum weight.
REFERENCES:
1. Iyengar. N.G.R and Gupta. S.K, “Structural Design Optimization”, Affiliated East West Press Ltd, New Delhi, 1997
2. Rao, S.S. “Engineering Optimization: Theory and Practice”, Fourth Edition, Wiley Eastern (P) Ltd., 2013.
3. Spunt, “Optimization in Structural Design”, Civil Engineering and Engineering Mechanics Services, Prentice-Hall, New Jersey 1971.
4. Uri Kirsch, “Optimum Structural Design”, McGraw Hill Book Co. 1981.
5. Haftka, R. T. and Gurdal, Z., Elements of Structural Optimization, Springer, 3 rd Edition, 1992