MultiPhysicsVault/.raw/AContinuumMechanicsBasedFourNodeShell/AContinuumMechanicsBasedFourNodeShell_002.md

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Int 4x2x2

(a)
Model I - distorted

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(b)
Model III - distorted
Figure 12: Large deflection analysis of a cantilever using distorted elements

Table 8 Results for large deflection analysis of a cantilever using distorted elements

	Model I (distorted)			Model III (distorted)
	step 2	step 5	step 8	step 2	step 5	step 8
$\phi^{FEM}/\phi^{analyt}$	0.13	0.13	0.13	0.95	0.84	0.76
$u^{FEM}/u^{analyt.}$	0.01	0.01	0.01	0.89	0.68	0.56
$w^{FEM}/w^{analyt}$	0.10	0.11	0.12	0.95	0.86	0.81
$\phi^{analyt}$	18°	45°	72°	18°	45°	72°

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P 2a h 2a R1 R2

(a) Spherical shell

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Central deflection, Wc	Central load, (P/1000)
0	0
50	30
100	45
150	50
200	40
250	35
300	55

(b) Non-linear load displacement curve.
Figure 13 Geometric non-linear response of a spherical shell. O, Horrigmoe; —, Leicester; ●, nine 4-node elements; □, one 16-node element Int 4×4×2

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ε ε 102. 54. 0.54 0.5 4

(a) Stiffened plate

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Vertical displac. of center	τ/τ_CR
0.004	0.95
0.008	1.00
0.012	1.00
0.016	1.00
0.020	1.00

(b) Large deflection response
Figure 14 Non-linear response of a stiffened plate. E=2.1\times10^{6} ; v=0.3

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hinged immovable edge

(a) 4-node shell model

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t R

(b) Axisymmetric model

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Vertical displac. of center	P
0	0
1	1500
2	2500
3	1000
4	1200
5	1300
6	1400
7	1500
8	1600
9	1700
10	1700

(c) Elastoplastic load-displacement curve
Figure 15 Response of elastic-perfectly plastic circular plate subjected to a concentrated load, P, at its centre. TLF abbreviates use of total Lagrangian formulation and MNO abbreviates use of materially non-linear-only formulation. R=100, t=1; E=2.1\times10^{6} ; E_{T}=0.0 ; \nu=0.3 ; \sigma_{\nu}=1000 . Circular plate response; —, axisymmetric model;
●, 4-node shell model

tive integration displacement models for nonlinear analysis of curved beams, Int. J. Num. Meth. Eng., 17, 615–631 (1981)
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