This paper proposes a new shell element formulation using the scaled boundary finite element (SBFE) method. A shell element is treated as a three-dimensional continuum. Its bottom surface is approximated with a quadrilateral spectral element and the shell geometry is represented through normal scaling of the bottom surface. Neumann expansion is applied to approximate the inversions of the matrix polynomials of the thickness coordinate xi, including the Jacobian matrix and the coefficient of the second-order term in the SBFE equation. This permits the solution along the thickness to be expressed as a matrix exponential function whose exponent is a high-order matrix polynomial of xi. After introducing the boundary conditions on the top and bottom surfaces and evaluating the resulting matrix exponential via Pade expansion, we derive the element stiffness and mass matrices. Poisson thickness locking is avoided fundamentally. Numerical examples demonstrate the applicability and efficiency of the formulation.
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页码:679 / 702
页数:24
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[31]
Macneal RH., 1985, FINITE ELEM ANAL DES, V1, P3, DOI [10.1016/0168-874X(85)90003-4, DOI 10.1016/0168-874X(85)90003-4]
机构:
Ho Chi Minh City Univ Technol, VNU HCMC, Fac Sci Appl, Dept Engn Mech, Ho Chi Minh City, VietnamHo Chi Minh City Univ Technol, VNU HCMC, Fac Sci Appl, Dept Engn Mech, Ho Chi Minh City, Vietnam
Nguyen, Khuong D.
;
Nguyen-Xuan, H.
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机构:
Duy Tan Univ, Da Nang, Vietnam
Sejong Univ, Dept Architectural Engn, Seoul 143747, South KoreaHo Chi Minh City Univ Technol, VNU HCMC, Fac Sci Appl, Dept Engn Mech, Ho Chi Minh City, Vietnam
机构:
Ho Chi Minh City Univ Technol, VNU HCMC, Fac Sci Appl, Dept Engn Mech, Ho Chi Minh City, VietnamHo Chi Minh City Univ Technol, VNU HCMC, Fac Sci Appl, Dept Engn Mech, Ho Chi Minh City, Vietnam
Nguyen, Khuong D.
;
Nguyen-Xuan, H.
论文数: 0引用数: 0
h-index: 0
机构:
Duy Tan Univ, Da Nang, Vietnam
Sejong Univ, Dept Architectural Engn, Seoul 143747, South KoreaHo Chi Minh City Univ Technol, VNU HCMC, Fac Sci Appl, Dept Engn Mech, Ho Chi Minh City, Vietnam