Calculation method

Element

Background

Convergence of solution

Convex plain 4-nodal thin plate/shell element used for static and free vibrations calculation.

Convex plain modified element designed by Fraeijs de Veubeke which correspond theory Kirchhoff (thin plates) is used. Element represents five nodal displacements: X’, Y’, Z’, X’r, Y’r in the local element space and, after global transformation, six nodal displacements: X, Y, Z, Xr, Yr, Zr in the global coordinate space.

Element stiffness matrix is build separately for X’-Y’ (Strain – Stress) and Z’-X’r-Y’r (Bending). Integration in the element – numerical.

Calculation of results as σx, σy, σxy (Stress-Strain), Mx, My, Mxy, Vx, Vy (Bending) is represented in the center of gravity of an element.  

u - displacements;

σ - stresses/forces;

||u|| - square root from square of  the integral of u in domain of an element;

Means, by refine of meshing net for  two times possible error for displacements is decreasing four times, error for stresses (forces)  - two times.  

Moderately thick

Thin

Very thin

t/l_x , t/l_y

1/5  to  1/10

1/5  to  1/50

< 1/50

Description

With transverse shear deformation

Without transverse shear deformation, mostly used for practical applications

Geometrically non-linear, with membrane deformation

Theory

Reissner, Mindlin

Kirchhoff

von Karman

Related beam theory

Timoshenko

Euler, Bernoulli

Theory of second order