Bending properties

Consider a loading consisting of bending loads only. In this case, the relationship between moments and curvatures can be rewritten:

where the matrix [d] is the 3×3 submatrix corresponding to lines and columns 4 through 6 of the inverse of the [ABD] matrix. In order to define an equivalent laminate bending modulus in the X direction, it is necessary to apply the following loads:

• Mx ≠ 0

• My = Mxy = 0

For this loading condition, one obtains:

If this loading condition were to be applied to an isotropic plate, the following curvature κx would be obtained:

Equating the expressions of κx given in the last two equations allows to define an equivalent bending Young’s modulus in the X direction:

To obtain an equivalent Poisson’s ratio in bending, one writes:

Similarly, to define an equivalent bending Young’s modulus in the Y direction, one must apply the following loading case:

• My ≠ 0

• Mx = Mxy = 0

For this loading condition, one obtains:

If this loading condition were to be applied to an isotropic plate, the following curvature κy would be obtained:

Equating the expressions of κy given in the last two equations allows to define an equivalent bending Young’s modulus in the Y direction:

To obtain the laminate equivalent bending shear modulus, , one must apply the following loading case:

• Mxy ≠ 0

• Mx = My = 0

Following an approach identical to the one presented above, one obtains:

Look up more details

Membrane properties

Transverse shear properties

Coefficients of thermal expansion

Other properties

Quick links

Command reference

Pre/Post video examples

Bulk Entry Descriptions

Simcenter 3D tutorials

Browse Simcenter 3D help by product area

Bending properties, Simcenter 3D 2021.1 Series

© 2020 Siemens

window.mainLanguage="en_US"

window.delivId=""

window.projectId=""

MathJax.Hub.Config({ TeX: { extensions: ["autoload-all.js"] }, tex2jax: { displayMath: [ ] }, "SVG": { scale: 125 } });