Theoretical Solution of Elastic Foundation Beam based on the Principle of Minimum Complementary Energy

To simplify and solve the problem of the foundation beam, a half-space elastic foundation beam was selected, and the elastic foundation beam was systematically explored based on Boussinesq solution and the principle of minimum complementary energy. The step-by-step loading method was adopted to derive the settlement formula of the foundation beam. The superposition principle was used and the flexibility influence matrix was introduced to obtain the deformation energy of the foundation beam under the action of external force, and the complementary energy functional of foundation beam was established. Combined with the engineering example, the force and settlement of the foundation beam under the concentrated load and uniform load were calculated respectively, and the distribution characteristic of the ground reaction was analysed. Results show that the linear homogeneous differential equations with ground reaction as the basic unknown quantity are established and the method for solving the ground reaction is given. The comparison analysis proves that the new method is accurate and feasible. The new algorithm using the principle of minimum complementary energy can provide a reference for solving the similar engineering problems. © 2021 School of Science, IHU. All rights reserved.