Table 1 Various loading \(q\), soil stiffness, and support conditions for the five cases
From: Nonlinear analysis of Euler beams resting on a tensionless soil with arbitrary configurations
Case | Load q | Number of lift-off points | \(\overline{K}\) | Support condition |
|---|---|---|---|---|
1 | \(U\left(x\right)\) | 0 | 500 | Clamped–clamped |
2 | \(U\left(x\right)-2U\left(x-\frac{1}{2}\right)\) | 1 | 500 | Clamped–clamped |
3 | \(U(x)-2U\left(x-\frac{1}{3}\right)+2.5U\left(x-\frac{2}{3}\right)\) | 2 | 500 | Clamped–clamped |
4, 5 | \(\left(U\left(x-\frac{3}{10}\right)-U\left(x-\frac{7}{10}\right)\right)\times \left(\frac{9375{x}^{4}}{32}-\frac{9375{x}^{3}}{16}+\frac{26625x2}{64}-\frac{7875x}{64}+\frac{6615}{512}\right)\) | 2 | 1250 | Free-free |