Advanced formulation for laminated composite shells: 3D stress analysis and rigid-body motions

A sampling surfaces method and its implementation for 3D thermal stress analysis of functionally graded plates

“…The SaS method with the arbitrary number of equispaced SaS is considered in [44]. The more general approach with the SaS located at Chebyshev polynomial nodes has been developed later [27,28]. Note also that the term SaS should not be confused with such terms as a mathematical surface or a virtual surface, which are extensively utilized in Carrera's unified formulation.…”

“…According to the SaS method [27,28], we choose inside the nth layer I n not equally spaced SaS X ðnÞ1 ; X ðnÞ2 ; . .…”

Exact geometry solid-shell element based on a sampling surfaces technique for 3D stress analysis of doubly-curved composite shells

“…In the present paper, the hybrid-mixed GeX four-node solid-shell element formulation is proposed in which the SaS are located inside each layer at Chebyshev polynomial nodes [5]. To circumvent locking phenomena, the assumed interpolations of displacement-independent strains and stress resultants are invoked and utilized together with displacement and displacement-dependent strain interpolations into the Hu-Washizu variational equation.…”

“…The SaS formulation with the arbitrary number of equispaced SaS is considered in [10]. The more general approach with the SaS located at the Chebyshev polynomial nodes was developed later [3][4][5]. In contribution [11], both SaS formulations are compared with each other.…”

“…Such choice of displacements with the consequent use of the Lagrange polynomials of degree In − 1 in the thickness direction for each layer allows the presentation of governing equations of the layered shell formulation in a very compact form. The SaS concept was proposed recently by the authors to evaluate analytically the 3D stress state in rectangular plates and cylindrical and spherical shells [3][4][5]. It should be noticed that the SaS shell formulation with equally spaced SaS does not work properly with the Lagrange polynomials of high degree because of the Runge's phenomenon [6].…”