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This paper aims to investigate post-buckling responses of shell-like structures using an implicit conservative-decaying time integration dynamic scheme.

In this work, the authors have proposed the use of a four-node quadrilateral flat shell finite element with drilling rotational degree of freedom within the framework of an updated Lagrangian formulation mutually with an implicit conservative-dissipative time integration dynamic scheme.

Several numerical simulations were considered to evaluate the accuracy, robustness, stability and the capacity of the considered time integration scheme to dissipate numerical noise in the presence of high frequencies. The obtained results illustrate a very satisfying performance of the implicit conservative-dissipative direct time integration scheme conjointly with the quadrilateral flat shell finite element with drilling rotation.

The authors have investigated the potential of the implicit dynamic scheme to deal with unstable branches after limit points in the non-linear post-buckling response of shell structures with no need for structural damping. The capability of the studied algorithm to study buckling and post-buckling behaviour of thin shell structures is illustrated through several numerical examples.

The purpose of this paper is to study the effect of the relative density and geometric parameters on the homogenised in-plane elasticity modulus of a cellular honeycomb structure using analytical and numerical approaches.

In this work, the mechanical behaviour of a new design of the honeycomb is analysed through a refined analytical model that is developed based on the energy theorems by considering the shearing and stretching effects in addition to bending.

By taking into account the various deformation mechanisms (MNT), the obtained results show that the values of elasticity modulus are the same for low relative densities, but the difference becomes remarkable for higher densities. Moreover, it is difficult to judge the effect of the relative density and anisotropy of the cellular structure on the values of the homogenised elasticity modulus without considering all the three deformation mechanisms in the analytical model. It is shown that conventional models overestimate the elasticity modulus, especially for high relative densities.

In this paper, a refined model that takes into account the three deformation mechanisms (MNT) is developed to predict the in-plane elasticity modulus of a honeycomb cellular material. It is shown that analytical models that describe the anisotropic behaviour of honeycomb cells can be improved by considering the three deformation mechanisms, which are bending, stretching, and shearing deformations.

This paper aims to describe the formulation of a displacement-based triangular membrane finite element with true drilling rotational degree of freedom (DOF).

The presented formulation incorporates the true drilling rotation provided by continuum mechanics into the displacement field by way of using the polynomial interpolation. Unlike the linked interpolation, that uses a geometric transformation between displacement and vertex rotations, in this work, the interpolation of the displacement field in terms of nodal drilling rotations is obtained following an unusual approach that does not imply any presumed geometric transformation.

New relationship linking the mid-side normal displacement to corner node drilling rotations is derived. The resulting new element with true drilling rotation is compatible and does not include any problem-dependent parameter that may influence the results. The spurious zero-energy mode is stabilized in a careful way that preserves the true drilling rotational degrees of freedom (DOFs).

Several works dealing with membrane elements with vertex rotational DOFs have been published with improved convergence rate, however, owing to the need for incorporating rotations in the finite element meshes involving solids, shells and beam elements, having finite elements with true drilling rotational DOFs is more appreciated.

nonlinear dynamic analysis of triangular and quadrilateral membrane elements with in-plane drilling rotational degree of freedom.

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.

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.

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.