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<p>In this paper, the three-dimensional (3D) stress analysis of layered doubly curved shells through a strong sampling surfaces (SaS) formulation is presented. The SaS method is based on the choice of SaS parallel to the middle surface and located at Chebyshev polynomial nodes inside the layers, to introduce the displacements of these surfaces as unknown functions that leads to a non-conventional 3D shell formulation. This is due to the use of Lagrange polynomials to interpolate displacements, strains and stresses in the thickness direction. Since the outer surfaces and interfaces are not included into a set of SaS, this makes it possible to uniformly minimize the error caused by using high-order Lagrange interpolation. To integrate the equilibrium equations of elasticity written in terms of SaS variables, the extended differential quadrature (EDQ) method proposed recently by the author can be applied, which opens up possibilities for high-precision calculations of layered doubly curved shells with general boundary conditions. This is due to the fact that in the SaS/EDQ formulation, the displacements, strains and stresses of SaS are interpolated in a rectangular domain specified in a curvilinear coordinate system using the Chebyshev–Gauss–Lobatto grid and Lagrange polynomials are utilized as basis functions. It is worth noting that the developed SaS/EDQ formulation deals with elasticity equilibrium equations in terms of SaS stresses avoiding the costly integration of second-order differential equations in terms of SaS displacements using the generalized differential quadrature (GDQ) method.</p>

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Elasticity solutions for sandwich and laminated composite doubly curved shells through strong sampling surfaces formulation

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • G. M. Kulikov

摘要

In this paper, the three-dimensional (3D) stress analysis of layered doubly curved shells through a strong sampling surfaces (SaS) formulation is presented. The SaS method is based on the choice of SaS parallel to the middle surface and located at Chebyshev polynomial nodes inside the layers, to introduce the displacements of these surfaces as unknown functions that leads to a non-conventional 3D shell formulation. This is due to the use of Lagrange polynomials to interpolate displacements, strains and stresses in the thickness direction. Since the outer surfaces and interfaces are not included into a set of SaS, this makes it possible to uniformly minimize the error caused by using high-order Lagrange interpolation. To integrate the equilibrium equations of elasticity written in terms of SaS variables, the extended differential quadrature (EDQ) method proposed recently by the author can be applied, which opens up possibilities for high-precision calculations of layered doubly curved shells with general boundary conditions. This is due to the fact that in the SaS/EDQ formulation, the displacements, strains and stresses of SaS are interpolated in a rectangular domain specified in a curvilinear coordinate system using the Chebyshev–Gauss–Lobatto grid and Lagrange polynomials are utilized as basis functions. It is worth noting that the developed SaS/EDQ formulation deals with elasticity equilibrium equations in terms of SaS stresses avoiding the costly integration of second-order differential equations in terms of SaS displacements using the generalized differential quadrature (GDQ) method.