Contact of a Flat Spring

Let us consider a flat spring, composed of two parts. The length of the first plate is 3L , the length of the second one is 2L. The plates have the same width b and the same height h. The plates are fixed on the left side and are loaded with the force P on the opposite side (see figure). It is supposed, that the plates are not tied together. Each plate can freely move by other one (without friction).

Let us use the following initial data: the length L is 0.05 m , the width b is 0.05 m, the height h of the each plate is 0.005 m and the magnitude of the applied force P is 100 N.
Material properties are the Young's modulus E = 2.1E+011 Pa and Poisson's ratio ν = 0.28.
The maximal vertical displacement Δz can be calculated: Δz= 118*P*L3 / 24*E*J , where P is the applied force, L is the length, J is the axial moment of inertia.
J= b*h3/12, where b is the width and h is the height of each plate.
The calculation using the above mentioned formulas gives the result:  Δz = 5.6190E-004 m .
After carrying out calculations by the AutoFEM Analysis the following results are obtained:

Table 1.Parameters of the finite element mesh

Table 2.The result “Displacement OZ”*

Conclusions:

The relative error of the numerical solution compared to the analytical solution is equal to 2.84% for quadratic finite elements.

*The results of numerical tests depend on the finite element mesh and may differ slightly from those given in the table.

 

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