Table 12 Coefficients \({a}_{i}\) for various \(N\) of Rayleigh–Ritz procedure in case (4)
From: Nonlinear analysis of Euler beams resting on a tensionless soil with arbitrary configurations
Coefficients \({a}_{i}\) | \(N=15\) | \(N=11\) | \(N=9\) |
|---|---|---|---|
\({a}_{1}\) | \(-12.11644098\) | \(-0.2443290684\) | \(0.02564239328\) |
\({a}_{2}\) | \(23.16072979\) | \(0.4598013053\) | \(-0.04768563563\) |
\({a}_{3}\) | \(-20.20919553\) | \(-0.3823959623\) | \(0.03834732574\) |
\({a}_{4}\) | \(16.07137737\) | 0.2798265612 | \(-0.02646196004\) |
\({a}_{5}\) | \(-11.61393415\) | \(-0.1789399189\) | \(0.01520990135\) |
\({a}_{6}\) | \(7.592365735\) | \(0.09856403472\) | \(-0.007169912679\) |
\({a}_{7}\) | \(-4.461734475\) | \(-0.0457998286\) | \(0.002646214949\) |
\({a}_{8}\) | \(2.336536222\) | \(0.01738868058\) | \(-6.705508312\times {10}^{-4}\) |
\({a}_{9}\) | \(-1.077289308\) | \(-0.005086442519\) | \(8.407102566\times {10}^{-5}\) |
\({a}_{10}\) | \(0.4299316184\) | \(0.001014930822\) | – |
\({a}_{11}\) | \(-0.1448997899\) | \(-1.020244299\times {10}^{-4}\) | – |
\({a}_{12}\) | \(0.03971007583\) | – | – |
\({a}_{13}\) | \(-0.008307533284\) | – | – |
\({a}_{14}\) | \(0.001177597947\) | – | – |
\({a}_{15}\) | \(-8.441222046\times {10}^{-5}\) | – | – |