A Seminalytical Approach to Large Deflections in Compliant Beams under Point Load

Table 1

Comparison of large deflection results in cantilever beams under free end point load using a linear model and the presented method, showing the absolute error and accuracy as compared to the well-established Richardson numerical solution (Richardson extrapolation) [24], as well as the number of polynomials, n, required for an accuracy of at least 99.00%.

	Linear solution		Presented method
𝛼	Absolute error	Accuracy (%)	Absolute error	Accuracy (%)	Number of polynomials, n, required for accuracy of 99%
0.1	5E-5	99.90	4E-10	99.99	1
0.2	4E-4	99.63	5E-9	99.99	1
0.3	11E-3	99.18	2E-8	99.99	1
0.4	34E-3	98.55	3E-8	99.99	2
0.5	56E-3	97.76	3E-8	99.99	3
0.6	96E-3	96.81	2E-8	99.99	3
0.7	1E-2	95.71	2E-7	99.99	4
0.8	3E-2	94.47	6E-7	99.99	4
0.9	3E-2	93.10	2E-6	99.99	4
1.0	4E-2	91.62	1E-5	99.99	4
1.1	5E-2	90.02	5E-5	99.99	5
1.2	6E-2	88.33	2E-4	99.96	5
1.3	8E-2	86.54	7E-4	99.86	6
1.4	9E-2	84.67	2E-3	99.63	7
1.5	1E-1	82.40	5E-3	99.21	8