Novel techniques for improving the interpolation functions of Euler-Bernoulli beam

In this paper, the efficiency and the accuracy of classical (CE) and high order (HE) beam element are improved by introducing two novel techniques. The first proposed element (FPE) provides an alternative for (HE) by taking the mode shapes of the clamped-clamped (C-C) beam into account. The second proposed element (SPE) which could be utilized instead of (CE) and (HE) considers not only the mode shapes of the (C-C) beam but also some virtual nodes. It is numerically proven that the eigenvalue problem and the frequency response function for Euler-Bernoulli beam are obtained more accurate and efficient in contrast to the traditional ones.