Unit 1 Finite Element Method

3 lecture hours

• Comparison with other methods
• General steps of FEM, Applications and Advantages

Unit 2 Introduction to the Stiffness (Displacement) Method

7 lecture hours

• Definition of the Stiffness Matrix
• Derivation of the Stiffness Matrix for a Spring Element
• Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method)
• Boundary Conditions
• Potential Energy Approach to Derive Spring Element Equations
• Examples of a Spring Assemblages

Unit 3 Development of Truss Equations– Introduction, Derivation of the Stiffness Matrix for a

7 lecture hours

• Bar Element in Local Coordinates
• Selecting Approximation Functions for Displacements
• Transformation of Vectors in Two Dimensions
• Global Stiffness Matrix formulation
• Computation of Stress for a Bar in the x-y Plane
• Solution of a Plane Truss
• Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space
• Use of Symmetry in Structure
• or Skewed
• Potential Energy Approach to Derive Bar Element Equations
• Comparison of Finite Element Solution to Exact Solution for Bar

Unit 4 Development of Beam Equations –Introduction, Beam Stiffness, Example of Assemblage

• of Beam Stiffness Matrices
• Examples of Beam Analysis Using the Direct Stiffness Method
• Distributed Loading
• Comparison of the Finite Element Solution to the Exact Solution for a Beam
• Beam Element with Nodal Hinge
• Potential Energy Approach to Derive Beam Element Equations. 10 Subject Code: 3172008 w.e.f