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  • Testing the finite element of the mixed method for calculation flat rod systems taking into account physical nonlinearity. Part I: Statically definable systems

    The article presents the approbation of the previously proposed algorithm for calculating flat rod systems whose cross sections have one axis of symmetry and the material is physically nonlinear. The diagram of the relationship between stresses and strains corresponds to an ideal elastoplastic material or an elastoplastic material with hardening. The calculation algorithm is based on the developed finite element of the mixed method. Examples of calculating statically determinable rod systems are given.

    Keywords: finite element of the mixed method, elastoplastic material, physical nonlinearity

  • Algorithm of the mixed method for determining the deflections in wooden beams, taking into account the long loading

    TThe article presents an algorithm for determining deflections in wooden beams of rectangular cross-section, taking into account the long load. The calculation algorithm is based on the proposed approach of D. Arleninov to specify the modulus of elasticity of wood, depending on the level of design stresses in tabular form. The aim of the research is to develop a software – oriented algorithm for calculating deflections of wooden beams under long-term loading. The object of study – a wooden beam of rectangular cross-section, located in a single load; the modulus of elasticity of the material varies both in length and height of the beam, depending on the level of design stresses. The algorithm uses the FEM of a mixed method with a variable length modulus of elasticity. The stiffness characteristics of the cross sections are refined during the calculation by a two-stage algorithm. Examples of the calculation of simply supported beams under various conditions of loading. The results of comparison with the experimental data of other authors indicate the correct operation of the proposed algorithm; the discrepancy between the numerical results and the experimental results is in the range from 0,31% to 11,6 %. This algorithm can also be used to clarify deflections and internal forces in flat statically indeterminate rod systems, whose modulus of elasticity varies depending on the acting stresses

    Keywords: finite element of the mixed method, variable modulus of elasticity, deflection of wooden beams, long-term loading