Course Details
Subject {L-T-P / C} : CE6033 : Numerical Methods in Civil Engineering { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Mahendra Gattu
Syllabus
Solution of large system of equations, Direct and Indirect method, Crammers Method, Gauss Elimination Method, Gauss Jordan method, Cholesky’s method, Gauss seidel method, Jacobi method, successive over relaxation technique, Programming Examples, Storage schemes, Band form, skyline form, Band solver technique, Cholesky’s L-U decomposition in skyline storage, Static Condensation technique, Submatrix equation solver, substructure concept, Numerical Interpolation, Lagrangian, Hermitian, Cubic spline, Numerical integration, deflection of beams, Gauss quadrature method, one-two-three point integrations, Deflection of cantilever, simply supported beam, Integration in two dimensions, Solution techniques for Eigen value problems, Vector iteration, power method, forward iteration, inverse iteration, Transformation method, Jacobi, Given method, Transformation matrices, Generalized eigen value problem, standard form, Approximate solution technique, static condensation, Rayleigh-Ritz method, subspace iteration, Application of finite difference method to buckling load of columns, deflection of beams and plates, Application of finite element method to statically indeterminate beam, beam with varying moment of inertia, plate deflection problems, solution of equilibrium equations in dynamics, direct method, central difference method, Houbolts method, Wilson method, Newmarks method
Course Objectives
- This course attempts to give a broad background to numerical methods common to various branches of civil engineering. <br />It starts with core concepts of error estimate and accuracy of numerical solutions. It then introduces the student to methods of solution of linear and non-linear equations.Both direct and iterative solution methods are discussed. <br />Next we introduce the numerical solution of partial differential equations, after a brief review of canonical partial differential equations and well known analytical techniques for their solution, stressing when and why numerical solutions are necessary. <br /> <br />Finite difference operators are introduced and used to solve typical initial and boundary value problems. <br /> <br />Following this we introduce the finite element method as a generic method for the numerical solution of partial differential equations. <br /> <br />The concepts of weak form, finite element discretization, polynomial interpolation using Lagrange polynomials and numerical quadrature are introduced. <br /> <br />Numerical integration in the time domain is discussed, emphasizing the key requirements of stability and accuracy of time integration algorithms. <br /> <br />Finally we discuss integral equations and introduce numerical techniques for their solution.
Course Outcomes
1. Students will be able to apply knowledge of mathematics, science and engineering <br />2. Students will be able to identify, formulate and solve civil engineering problems
Essential Reading
- Timothy Sauer, Numerical Analysis, Pearson Education Inc, Boston, MA
- D. Dahlquist, and A. Bork, Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ
Supplementary Reading
- Jorge Nocedal, and Stephen J. Wright, Numerical Optimization, Spring-Verlag New York, Inc.
- I. Stakgold, Green's functions and Boundary Value Problems, Wiley