Shear deformable plate elements based on exact elasticity solution. (15th April 2018)

• Record Type: Journal Article
• Authors: Karttunen, Anssi T.; von Hertzen, Raimo; Reddy, J.N.; Romanoff, Jani
• Is Part Of: Computers & structures. Volume 200(2018)
• Page Start: 21
• Page End: 31
• Publication Date: 2018-04-15
• Subjects: Interior plate -- Boundary layer -- Galerkin's method -- Finite element -- Eigenvalues; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2018.02.006
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: General 3-D elasticity solution is used to develop locking-free 2-D rectangular plate finite elements. The Mindlin, Levinson and Full Interior plate theories at hand share the same shape functions. The shape functions satisfy the plate equilibrium equations and Kirchhoff constraints exactly. Linked interpolations provide high-order expansions of the displacement variables. Linear bending, buckling and free vibration problems are studied numerically. Abstract: The 2-D approximation functions based on a general exact 3-D plate solution are used to derive locking-free, rectangular, 4-node Mindlin (i.e., first-order plate theory), Levinson (i.e., a third-order plate theory), and Full Interior plate finite elements. The general plate solution is defined by a biharmonic mid-surface function, which is chosen for the thick plate elements to be the same polynomial as used in the formulation of the well-known nonconforming thin Kirchhoff plate element. The displacement approximation that stems from the biharmonic polynomial satisfies the static equilibrium equations of the 2-D plate theories at hand, the 3-D Navier equations of elasticity, and the Kirchhoff constraints. Weak form Galerkin method is used for the development of the finite element model, and the matrices for linear bending, buckling and dynamic analyses are obtained through analytical integration. In linear buckling problems, the 2-D Full Interior and Levinson plates perform particularly well when compared to 3-D elasticity solutions. Natural frequencies obtained suggest that the optimal value of the shear correction factor of the Mindlin plate theory depends primarily on the boundary conditions imposed on the transverse deflection of the 3-D plate used to calibrate the shear correction factor.