Exact geometry SaS solid-shell element for 3D stress analysis of FGM piezoelectric structures

Abstract A hybrid-mixed functionally graded material (FGM) piezoelectric four-node solid-shell element through the sampling surfaces (SaS) method is proposed. The SaS formulation is based on choosing inside the shell N SaS parallel to the middle surface in order to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. Such choice of unknowns with the use of Lagrange polynomials of degree N-1 in through-thickness interpolations of the displacements, strains, electric potential, electric field and material properties leads to a robust FGM piezoelectric shell formulation. The inner SaS are located at Chebyshev polynomial nodes that make it possible to minimize uniformly the error due to Lagrange interpolation. To implement the effective analytical integration throughout the element, the extended assumed natural strain (ANS) method is employed. As a result, the piezoelectric four-node solid-shell element exhibits a superior performance in the case of coarse meshes. To circumvent shear and membrane locking, the hybrid stress-strain solid-shell formulation via the Hu-Washizu variational principle is employed. The developed solid-shell element could be useful for the 3D stress analysis of FGMstructures because the SaS method allows obtaining the solutions with a prescribed accuracy, which asymptotically approach the exact solutions of electroelasticity as the number of SaS tends to infinity.

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

Curved and Layered Structures ◽

10.1515/cls-2016-0001 ◽

2015 ◽

Vol 3 (1) ◽

Cited By ~ 3

Author(s):

G. M. Kulikov ◽

A. A. Mamontov ◽

S. V. Plotnikova ◽

S. A. Mamontov

Keyword(s):

Stress Analysis ◽

Numerical Solutions ◽

Variational Equation ◽

Shell Element ◽

Middle Surface ◽

Superior Performance ◽

Lagrange Polynomials ◽

Shell Formulation ◽

Coarse Meshes ◽

Doubly Curved

AbstractA hybrid-mixed ANS four-node shell element by using the sampling surfaces (SaS) technique is developed. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the displacements of these surfaces as basic shell variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In − 1 in the thickness direction for each layer permits the presentation of the layered shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. To implement the efficient analytical integration throughout the element, the enhanced ANS method is employed. The proposed hybrid-mixed four-node shell element is based on the Hu-Washizu variational equation and exhibits a superior performance in the case of coarse meshes. It could be useful for the 3D stress analysis of thick and thin doubly-curved shells since the SaS formulation gives the possibility to obtain numerical solutions with a prescribed accuracy, which asymptotically approach the exact solutions of elasticity as the number of SaS tends to infinity.

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Modeling and analysis of spiral actuators by exact geometry piezoelectric solid-shell elements

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x19880014 ◽

2019 ◽

Vol 31 (1) ◽

pp. 53-70

Author(s):

GM Kulikov ◽

SV Plotnikova ◽

E Carrera

Keyword(s):

Shell Element ◽

Middle Surface ◽

Solid Shell ◽

Modeling And Analysis ◽

Lagrange Polynomials ◽

Shell Elements ◽

Exact Geometry ◽

Piezoelectric Solid ◽

Assumed Natural Strain ◽

Shell Formulation

An exact geometry four-node piezoelectric solid-shell element through the sampling surfaces formulation is proposed. The sampling surfaces formulation is based on choosing inside the shell N – 2 sampling surfaces parallel to the middle surface and located at Chebyshev polynomial nodes to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. The bottom and top surfaces are also included into a set of sampling surfaces. Such choice of unknowns with the use of Lagrange polynomials of degree N – 1 in the through-the-thickness interpolations of displacements, strains, electric potential, and electric field yields a robust piezoelectric shell formulation. To implement efficient analytical integration throughout the solid-shell element, the extended assumed natural strain method is employed. The developed hybrid-mixed four-node piezoelectric solid-shell element is based on the Hu-Washizu variational principle and shows the excellent performance for coarse mesh configurations. It can be useful for the 3D stress analysis of piezoelectric shells with variable curvatures, in particular for the modeling and analysis of spiral actuators.

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