Frictional Slide Contact Element for Elastomeric Bearings of Prestressed Shallow Reticulated Shells during Construction

There are two main purposes to prestress a long/medium span column-supported shallow reticulated shell along its tensile stress trajectories or boundary edges: (1) to decrease its deflection and (2) to approximately make the shell a self-balance entity on the horizontal plane. The exerted prestressing forces make the columns mainly work at the compression state of little eccentricity under normal service conditions. When prestressing the shell during construction, large horizontal deflections occur at its supports. In some projects elastomeric bearings are adopted, for the bearings can also provide damping. Exact analysis of elastomeric bearing of frictional slide contact takes much time and the results are not easy to get. In the paper a simplified model of frictional slide contact elastic element is proposed. In the process of iteration, the discontinuous stiffness of the element is expressed as a hyperbolic tangent function for the benefit of computer programming: $$ K_H = \frac{{{}^{i + 1}GA}} {{2t_r }} + \frac{{{}^{i + 1}GA\tanh \left\lfloor {\kappa \left( {\mu {}_j^{i + 1} N - \left| {{}_j^{i + 1} P} \right|} \right)/(\mu {}_j^{i + 1} N)} \right\rfloor }} {{2t_r }} $$ An improved formula of imbalance force vector is used to accelerate the convergence of iterations: $$ \bar F = F - \sum\limits_m {R_2^m F^m } + $$ An actual structure is taken to verify the reliability of the frictional slide contact elements. Analysis shows that the relative errors between computed results and measured values are very small.