Purpose nonlinear dynamic analysis of triangular and quadrilateral membrane elements with in-plane drilling rotational degree of freedom. Design/methodology/approach The nonlinear analysis is carried out using the updated co-rotational Lagrangian description. In this purpose, in-plane co-rotational formulation that considers the in-plane drilling rotation is developed and presented for triangular and quadrilateral elements, and a tangent stiffness matrix is derived. Furthermore, a simple and effective in-plane mass matrix that takes into account the in-plane rotational inertia, which permit true representation of in-plane vibrational modes is adopted for dynamic analysis, which is carried out using the Newmark direct time integration method. Findings The proposed numerical tests show that the presented elements exhibit very good performances and could return true in-plane rotational vibrational modes. Also, when using a well-chosen co-rotational formulation these elements shows good results for nonlinear static and dynamic analysis. Originality/value Publications that describe geometrical nonlinearity of the in-plane behaviour of membrane element with rotational d.o.f are few, and often they are based on the total Lagrangian formulation or on the rate form. Also these elements, at the author knowledge, have not been extended to the nonlinear dynamic analysis. Thus, an appropriate extension of triangular and quadrilateral membrane elements with drilling rotation to nonlinear dynamic analysis is required.

The objective of this research is to evaluate the effects of soil‐structure interaction (SSI) on the modal characteristics and on the dynamic response of structures. The stress had an impact on the overall behaviour of five storeys reinforced concrete (R/C) buildings typically encountered in Algeria. Sensitivity studies are undertaken in order to study the effects of frequency content of the input motion, frequency of the soil structure system, rigidity and depth of the soil layer on the dynamic response of such structures. This investigation indicated that the rigidity of the soil layer is the predominant factor in soil‐structures interaction and its increases would definitely reduce the deformation of the R/C structures. On the other hand, increasing the period of the underlying soil will cause an increase in the lateral displacements at storey levels and create irregularity in the distribution of storey shears. Possible resonance between the frequency content of the input motion and soil could also play an important role in increasing the structural response.

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We present in this research article, the improvements that we made to create a four nodes flat quadrilateral shell element for geometrically nonlinear analysis, based on corotational updated lagrangian formulation. These improvements are initially related to the improvement of the in-plane behaviour by incorporation of the in-plane rotational degrees of freedom known as “drilling degrees of freedom” in the membrane displacements field formulation. In the second phase, a co-rotational spatial local system of axes which adapts well to the problems of quadrilateral elements is adopted, while ensuring simplicity and effectiveness at numerical level. The required goal being mainly to have a robust thin shell element associated with a simplified formulation. The obtained element remains economic, and showing a robust behaviour in delicate situations of tests.