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2D Element Thermal Loads

Thermal loads can be either a constant temperature rise in the whole element or a temperature gradient, varying over the surface element. To evaluate the equivalent nodal forces the temperatures have to be converted to strains, using the temperature coefficient of expansion. The strains are then related to the stress through the material matrix and then the internal stresses are integrated over the element. The thermal effects are the same in all directions so there are no shear strains introduced.

For in-plane effects (constant temperature) the strain is

εp=[εxxεyyγxy]=[αTαT0]\boldsymbol{\varepsilon}_{p} = \begin{bmatrix} \varepsilon_{xx} & \varepsilon_{yy} & \gamma_{xy} \\ \end{bmatrix} = \begin{bmatrix} \alpha T & \alpha T & 0 \\ \end{bmatrix}

For bending effects (temperature gradients) the strain and stress are

κb=[κxxκyyκxy]=1t[4αT4αT0]\boldsymbol{\kappa}_{b} = \begin{bmatrix} \kappa_{xx} & \kappa_{yy} & \kappa_{xy} \\ \end{bmatrix} = \frac{1}{t}\begin{bmatrix} 4\alpha T & 4\alpha T & 0 \\ \end{bmatrix}

These are converted to stresses through the material matrix

σp=Cpεpσb=Cbκb\boldsymbol{\sigma}_{p} = \mathbf{C}_{p}\boldsymbol{\varepsilon}_{p}\qquad\boldsymbol{\sigma}_{b} = \mathbf{C}_{b}\boldsymbol{\kappa}_{b}

Note: In GSA, loads can be applied to a list of members or elements. Any loads applied onto members will be automatically expanded into the appropriate elements loads in the solver in order to analyse the model.