The document discusses three criteria for the convergence of displacement/shape functions in the finite element method: 1) Displacement functions must be continuous and compatible within elements, with no discontinuities between elements. 2) Displacement functions must be capable of representing constant strain states within elements. 3) Displacement functions must be capable of representing rigid body displacements, with elements experiencing no strain and zero nodal forces under rigid body motion.

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
Convergence Criteria
of
Displacement/Shape Function

2. 1) Displacement function must be continuous and compatible within
elements.
Convergence Criteria of Displacement/Shape Function
Compatible: When it deforms, there should not be any
discontinuity between elements, i.e. Elements must not separate
or overlap and there should not be any sudden change in slope
across the inter element boundaries.
Continuous: Second element should start by taking one edge
common of first element.

3. 3) The displacement function must be capable of representing rigid
body displacement.
2) The displacement function must be capable of representing
constant strain state within the elements. This will achieved by
dividing structure into smaller and smaller elements.
i.e. when nodes are given such displacement under rigid body
motion, elements should not experience any strain and hence
leads to zero nodal force. Constant term in polynomial ensures this
condition.