TLS 01: Plate under temperature load

Description

Material	Modulus of elasticity Possion’s ratio	$E=200 000 N/mm^2$ $\upsilon = 0.3$
Material	Thermal dilation	$\alpha =0.000 010/ ^{\circ}C$
Geometry	Plate thickness	t=10mm
Geometry	Boundary conditions	Fixed along all sides
Loads		Lineair gradient in local y’ direction $\Delta T = 100 ^{\circ}C$
Mesh	Max. element size: Min. element size:	0,1m 0,0m

Open handcalculations

Calculate the bending stiffness
$D=\frac{E \cdot t^3}{12 \cdot \left ( 1-\upsilon ^2 \right )}=18.315 \text{kNm}$

$M_{xx}=-\frac{\alpha \cdot \Delta T\cdot \left ( 1+\upsilon \right )\cdot D}{t}= - 2381.0 \frac{N \cdot m}{m}$

$\sigma _{xx}=\frac{6 \cdot M_{xx}}{t^2} = -142.9 \frac{N}{mm^2}$

Bending moment $M_{xx}$ and stress $\sigma_{xx}$ calculated by Diamonds

	Independent reference	Diamonds	Difference
Bending moment in the local x’-direction $M_{xx}$	-2381.0 kNm	-2381.0 kNm	0%
Elastic stress in the local x’-direction $\sigma_{xx}$	-142.9 $\frac{N}{mm^2}$	-142.9 $\frac{N}{mm^2}$	0%

Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: HSLS 01: plaque mince se déformant suivant une surface sphérique
Timoshenko, S., & Woinowsky-Krieger, S. (1959). Theory of plates and shells. McGraw-Hill Publishing Company.
Timoshenko, S., & Woinowsky-Krieger, S. (1948). Strenght of Materials – PART II. D. Van Nostrand Company.

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