Exact 3D stress analysis of laminated composite plates by sampling surfaces method

Куликов, Г. М.; Плотникова, С. В.

doi:10.1016/j.compstruct.2012.06.006

Cited by 57 publications

(43 citation statements)

References 22 publications

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“…The data listed in Tables 1 and 2 show that the SaSGeX4 element allows reproducing the exact solution of elasticity [43] for thick and thin plates with a high accuracy by using a fine 64 64  mesh and the sufficiently large number of SaS. As can be seen, the SaSGeX4 element provides from four to five right digits for displacements and stresses except for the transverse normal stress comparing to authors' exact SaS solution [4]. Figure 6 displays the distributions of displacements and stresses (51) through the thickness of the plate for different values of the slenderness ratio h a / It is worth noting that the element stiffness matrix (49) requires only direct substitutions, i.e., no expensive matrix inversion is needed to derive it.…”

Section: Remarkmentioning

confidence: 81%

“…As can be seen, the SaSGeX4 element provides from four to five right digits for displacements and stresses except for the transverse normal stress comparing to authors' exact SaS solution [4]. Figure 6 displays the distributions of displacements and stresses (51) same 64 × 64 mesh.…”

Section: Laminated Composite Rectangular Plate Under Sinusoidal Loadingmentioning

confidence: 93%

“…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].…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Куликов

Mamontov

Плотникова

et al. 2015

Curved and Layered Structures

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A 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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Section: Remarkmentioning

confidence: 81%

Section: Laminated Composite Rectangular Plate Under Sinusoidal Loadingmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Куликов

Mamontov

Плотникова

et al. 2015

Curved and Layered Structures

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show abstract

“…To solve such a problem, the four-node quadrilateral plate element using the sampling surfaces (SaS) technique [14,15] is proposed. The SaS formulation is based on choosing inside the n th layer the arbitrary number of surfaces…”

Section: Introductionmentioning

confidence: 99%

Hybrid-Mixed Quadrilateral Element for Laminated Plates Composed of Functionally Graded Materials

Куликов¹,

Carrera²,

Плотникова³

2017

AMT

Self Cite

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A hybrid-mixed four-node quadrilateral element for the three-dimensional stress analysis of laminated functionally graded plates through the use of the method of sampling surfaces is developed. The sampling surfaces formulation is based on choosing inside the n th layer I n not equally spaced sampling surfaces parallel to the middle surface, in order to introduce the displacements of these surfaces as basic plate variables. The sampling surfaces are located inside each layer at Chebyshev polynomial nodes that allows one to uniformly minimize the error due to the Lagrange interpolation. To avoid shear locking and have no spurious zero energy modes, the assumed natural strain concept is employed. The developed assumed natural strain four-node quadrilateral plate element passes the bending patch tests for laminated and functionally graded plates and exhibits a superior performance in the case of coarse distorted mesh configurations. It can be useful for the three-dimensional stress analysis of thick and thin laminated functionally graded plates because the sampling surfaces formulation gives the possibility to obtain the numerical solutions with a prescribed accuracy, which asymptotically approach the three-dimensional exact solutions of elasticity as the number of sampling surfaces tends to infinity.

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A hybrid‐mixed four‐node quadrilateral plate element based on sampling surfaces method for 3D stress analysis

Куликов

Плотникова

2016

Numerical Meth Engineering

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SUMMARYThe hybrid-mixed assumed natural strain four-node quadrilateral element using the sampling surfaces (SaS) technique is developed. The SaS formulation is based on choosing inside the plate body N not equally spaced SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic plate variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree N -1 in the thickness direction permits the presentation of the plate formulation in a very compact form. The SaS are located at Chebyshev polynomial nodes that allow one to minimize uniformly the error due to the Lagrange interpolation. To avoid shear locking and have no spurious zero energy modes, the assumed natural strain concept is employed. The developed hybrid-mixed four-node quadrilateral plate element passes patch tests and exhibits a superior performance in the case of coarse distorted mesh configurations. It can be useful for the 3D stress analysis of thin and thick plates because the SaS formulation gives the possibility to obtain solutions with a prescribed accuracy, which asymptotically approach the 3D exact solutions of elasticity as the number of SaS tends to infinity.

show abstract

Exact 3D stress analysis of laminated composite plates by sampling surfaces method

Cited by 57 publications

References 22 publications

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

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

Hybrid-Mixed Quadrilateral Element for Laminated Plates Composed of Functionally Graded Materials

A hybrid‐mixed four‐node quadrilateral plate element based on sampling surfaces method for 3D stress analysis

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