DIFFERENT ALTERNATIVES TO OBTAIN THE STIFFNESS MATRIX IN THE TIMOSHENKO BEAM

ALEJANDRO T. BREWER; FERNANDO G. FLORES; ADRIANO TRONO ; SERGIO PREIDIKMAN

Concordia-Salto

Congreso; XXXIX Congreso Argentino de Mecánica Computacional y I Congreso Argentino Uruguayo de Mecánica Computacional (MECOM 2023); 2023

UTN, Argentina y UDELAR, Uruguay

Timoshenko’s beam theory assumes that the section remains plane after deformation and admits that the section does not remain normal to the deformed axis, which allows the inclusion of shear strains. In the framework of the finite element method the simplest approximation formulates elements having C0 continuity. Using appropriate remedies to avoid shear locking, these elements exhibit good behavior. In this work, the stiffness matrix of a beam element is obtained according to the hypotheses of the Timoshenko model by resorting to three alternatives: the integration of the differential equations of equilibrium, the force method and the principle of minimum total potential energy. The interpolation functions obtained show C1 continuity. The results are compared with those obtained using linear Lagrangian elements and some conclusions are stated.