Lect09
- 1. Dr. A. S. Sayyad Professor & Head Department of Structural Engineering Sanjivani College of Engineering, Kopargaon 423603. (An Autonomous Institute, Affiliated to Savitribai Phule Pune University, Pune) Finite Element Method In Civil Engineering Step by Step Procedure of Finite Element Analysis
- 2. Step by Step Procedure of FEM 1. Select suitable field variables and the elements 2. Discretize the Continuum 3. Select Interpolation Function 4. Find Element Properties 5. Assemble Global Properties 6. Impose the Boundary Condition 7. Make the additional calculations to get the required values
- 3. 1. Select suitable field variables (DOF) and the elements The basic unknowns or the field variables which are encountered in the engineering problem are, Displacement in solid mechanics, Velocities in fluid mechanics, Electric and magnetic potentials in electrical engineering, Temperature in heat transfer problem. 2) Discretize the Continuum/Structure 3) Select Interpolation/Displacement Function: The finite element procedure reduces infinite unknowns to a finite numbers by dividing domain into sub- domains called as elements and by expressing the unknown field variables in terms of assumed approximating/displacement function (Interpolating function /shape function) within each element.
- 4. 4) Find Element Properties: After selecting elements and nodal unknowns next step in finite element analysis is to assemble element properties for each element Example: element stiffness matrix, nodal displacement vector of element, and nodal force vector of element. Element properties can be assembled by four methods, 1. Direct approach 2. Variational approach 3. Weighted residual approach 4. Energy balance approach. 5) Assemble Global Properties: Element properties are used to assemble global properties to get system equations, Example: Global stiffness matrix, nodal displacement vector of structure, and nodal force vector of structure.
- 5. 7) Impose the Boundary Condition: The boundary conditions are imposed to find the solution of system equations which gives nodal unknowns. 8) Make the additional calculations to get the required values: Using nodal unknowns additional calculations are made to get the required values, e.g. stresses, strains, moments etc.