Deflection of a Plate under Pressure

Let us consider a plate under pressure load q. Dimensions are a b t. Sought quantity is the maximum deflection w1,2,3. Consider following cases:

1. One end is clamped, opposite end is simply supported, lateral ends are free.

Deflection of a Beam under a Uniformly Distributed Load

analytical solution is:

2. One edge is clamped, opposite edge is free, lateral edges are simply supported.

Deflection of a Beam under a Uniformly Distributed Load

analytical solution is:

3. One edge is clamped, the remaining edges are simply supported.

Deflection of a Beam under a Uniformly Distributed Load

analytical solution is:

Let us use the following initial data: q = 2000 Pa, a = 1000 mm, b=500 mm, t=1.5 mm.
Material characteristics: the Young's modulus E = 2.1E+011 Pa, G=8.203E+010 Pa, Poisson's ratio ν = 0.28.

Deflection of a Beam under a Uniformly Distributed Load, the finite element model with applied loads and restraints

The finite element model with applied loads and restraints

Thus, D=64.0869 N*m, Jx=1.4062E-010 m4,

w1=184.5503 mm,

w2=29.2571 mm,

w3=18.1394 mm.

After carrying out calculation with the help of AutoFEM, the following results are obtained:

Table 1.Parameters of the finite element mesh

Finite Element Type	Number of Nodes	Number of Finite Elements
linear triangle	2112	4032

Table 2. Result "Displacement"

Numerical Solution Displacement \| w1,2,3* \|, m	Analytical Solution Displacement \| w \|, m	Error δ =100%* \|w* - w \| / \| w \|
184.4077	184.5503	0.08
28.7067	29.2571	1.88
18.2513	18.1394	0.62

Deflection of a Beam under a Uniformly Distributed Load, Result "Displacement, Z"

Conclusions:

The relative error of the numerical solution compared to the analytical solution is equal to 1.92% for linear finite elements.

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