Unit 1 Finite Element Method

• history and application
• Comparison with other methods
• Variational approach
• Galerkin’s Methods. 3 7.5

Unit 2 Element and Boundary Condition

8 lecture hours

• Element shapes
• interpolation function
• Virtual energy principle
• Rayleigh- Ritz method
• stiffness matrix and properties
• Boundary conditions
• solution of system of equations
• shape functions and characteristics
• Basic equations of elasticity
• strain displacement relations 6 15 3 1-D structural problems – axial bar element – stiffness matrix
• load vector
• temperature effects
• Quadratic shape function
• Analysis of Trusses – Plane Truss and Space Truss elements 5 12.5 4 Analysis of beams – Hermite shape functions – stiffness matrix – Load vector – Problems. 2-D problems –CST, LST, force terms
• Stiffness matrix
• boundary conditions. 7 17.5 5 Element types - Isoparametric element – quadrilateral element
• Shape functions – Numerical Integration – sub parametric and super parametric elements. 3-D problems – Tetrahedral element – Jacobian matrix – Stiffness matrix. 6 15 6 Dynamic Analysis - Dynamic considerations
• Dynamic equations – consistent mass matrix – Eigen Values
• Eigen Vector
• natural frequencies – mode shapes – modal analysis
• Applications of numerical procedures to determine natural frequencies and mode shapes
• Finite Element Method for dynamic analysis
• Introduction to torsional problems 7 Introduction to Non linearity
• Geometric Non-linearity
• Material Non- linearity
• Non linear dynamic problems
• analytical problems 5 12.5