Linear and Nonlinear Stability Analysis of Thin Rectangular Plates Subjected to Local In-Plane Shearing

Figures & data

Fig. 1: Partially sheared rectangular thin plate

Table 1: Comparison between τ_cr values obtained analytically and those obtained in the present work

$\text{β}=a/b$	Critical buckling stress, τcr (MPa)		Relative errors (%)
	Analytical results	Present work results
2	119.760	123.500	3.123
3	109.266	110.200	0.855
4	105.593	106.130	0.509
5	103.893	104.350	0.440
6	102.969	103.390	0.409

Fig. 2: Variation of the linear critical shear buckling stress versus load aspect ratio α for different plate aspect ratios β

Table 2: Critical linear buckling stress obtained from the different mesh discretizations

Load case α (%)	Critical buckling stresses, τcr (MPa)			Relative errors (%)
	Mesh A	Mesh B	Mesh C	Mesh A	Mesh C
20	168.180	168.170	168.170	0.006	0.000
40	95.490	95.490	95.490	0.000	0.000
60	84.800	84.800	84.800	0.000	0.000
80	103.800	103.790	103.790	0.010	0.000
100	123.510	123.500	123.500	0.008	0.000

Fig. 3: Variation of critical buckling load (linear and nonlinear) τ_cr versus α ratio for plate with β = 2

Fig. 4: Variation of shear stress ${\tau }_{\mathrm{xy}}$ versus displacement w_max for plate with β = 2 and α = 20%, 40%, 60%, 80% and 100%

Table 3: The compressive and shear stress values (σ_{c max}, σ_{c min}, τ_xy) for a plate with β = 2 and α = 40%

		σc (MPa)		σc(x) / σc(y)		$\left|{\tau }_{\mathrm{xy}}\right|$ (MPa)
		σcmax (MPa)	σcmin (MPa)	σmax (x)/ σmax (y)	σmin (x) / σmin (y)	$\left|{\tau }_{\mathrm{xy}max}\right|$ (MPa)	$\left|{\tau }_{\mathrm{xy}min}\right|$ (MPa)
Linear FE analysis	In the x-direction	345.500	24.810	1.409	1.505	128.900	1.244
	In the y-direction	245.200	16.480
Nonlinear FE analysis	In the x-direction	278.900	19.250	1.142	1.497	146.700	47.050
	In the y-direction	244.200	12.860

Fig. 5: Nonlinear shear stress (10⁻² MPa) distribution throughout a plate specimen with β = 2 and α = 40%

Fig. 6: Plate under shear loading and Fig. 7. Equivalent plate under shear loading

Fig. 8: Nonlinear von Mises stress (10⁻² MPa) distribution at the first plasticization on a buckled plate specimen with β = 2, α = 40% and τ_xy = 94.709 MPa

Fig. 9: Nonlinear maximum von Mises stress (10⁻² MPa) distribution throughout a plate specimen value reached step with β = 2, α = 40% and τ_xy = 131.507 MPa

Fig. 10: Nonlinear von Mises stress (10⁻² MPa) distribution throughout a buckled plate specimen a few steps after reaching the maximum value with β = 2, α = 40% and τ_xy = 124.765 MPa

Data Availability Statement

The data that support the findings of this study are available from the first named author, upon reasonable request. Any such requests should be made by emailing the first named author directly.