VE 0016 | Elastic Bending – Continuous Load

Description

A thin plate is fully fixed on the left end and is subjected to a uniform pressure according to the sketch. The problem is described by the following set of parameters.

Material	Elastic	Modulus of Elasticity	E	210000.000	MPa
		Poisson's Ratio	ν	0.000	-
		Shear Modulus	G	105000.000	MPa
Geometry	Plate	Length	L	1.000	m
		Width	w	0.050	m
		Thickness	t	0.005	m
Load		Uniform Pressure	p	2.750	kPa

Small deformations are considered and the self-weight is neglected in this example. Determine the maximum deflection u_z,max. The aim of this example is to show that a surface of the surface stiffness type Without Membrane Tension behaves linearly under bending.

01 Elastic Bending – Continuous Load

Analytical Solution

The pressure p can be transformed into continuous line load q = pw. The maximum deflection of the cantilever loaded by the continuous load is defined as:

u_{z, \max} = \frac{q L^{4}}{8 E I_{y}} = \frac{3 p L^{4}}{2 E w^{2} t}

Maximum Deflection

RFEM Settings

Modeled in RFEM 5.04 and RFEM 6.01
The element size is l_FE = 0.020 m
Geometrically linear analysis is considered
The Mindlin plate theory is used
Isotropic linear elastic material model is used

Results

Surface Stiffness Type	Analytical Solution	RFEM 5		RFEM 6
Surface Stiffness Type	u_z,max [mm]	u_z,max [mm]	Ratio [-]	u_z,max [mm]	Ratio [-]
Standard	157.143	157.130	1.000	157.125	1.000
Without Membrane Tension	157.143	157.150	1.000	157.125	1.000

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