Shell dynamics with three-dimensional degenerate finite elements

Abstract

Abstract-An explicitly through the thickness integrated two-dimensional version of the three-dimensional degenerated she11 element is formulated here to study the dynamics of elastic shells. A nine-noded quadrilateral Lagrangian element is used with five degrees of freedom per node. A specialized mass diagonalization scheme, developed by Hinton, Rock and Zienkiewicz, is used which conserves the total mass of the element and also includes the effects of the rotary inertia terms. Hamilton's principle is used to derive the equations of motion. Mode superposition coupled with Duhamel's integral is first employed to obtain a solution of the equations of motion in time. Mode shapes and frequencies are computed by subspace iteration technique. Direct time integration using the implicit Newmark-P method is also carried out. Several examples are presented and the results obtained by mode superposition and direct time integration methods are compared.

Influence of Opening Locations on the Structural Response of Shear Wall

“…Nevertheless, the general shell theory based on the classical approach has been found to be complex in the finite element formulation. On the other hand, the degenerated shell element [19,20] derived from the threedimensional element has been quite successful in modeling moderately thick structures because of their simplicity and circumvents the use of classical shell theory. The degenerated shell element is based on assumption that the normal to the Journal of Nonlinear Dynamics mid-surface remain straight but not necessarily normal to the mid-surface after deformation.…”

Dynamic analysis of squat shear wall using nonlinear finite element method

“…Nevertheless, the general shell theory based on the classical approach has been found to be complex in the finite element formulation. On the other hand, the degenerated shell element (Ahmad et al 1970, Kant et al 1994 derived from the three-dimensional element has been quite successful in modeling moderately thick structures because of their simplicity and has circumvented the use of classical shell theory. The degenerated shell element ( Figure 1) is based on the assumption that the normal to the middle surface remains straight but not necessarily normal after deformation.…”

“…Hence, it can be observed that γ¯ξδ is linear in ξ direction and quadratic in ε direction, while γ¯εδ is linear in ε direction and quadratic in ξ direction. The polynomial terms for curvature of nine-node Lagrangian element, κ ξ and κ ε , are the same as the assumed shear strain as given by κξ=∂ζξ (1,ξ,ε,ξε,ξ2,ξ2ε,ε2,ξε2,ξ2ε2)∂ξκξ=κξ (1,ξ,ε,ξε,ε2,ξε2) (15) κε=∂ζε (1,ξ,ε,ξε,ξ2,ξ2ε,ε2,ξε2,ξ2ε2)∂εκε= (1,ξ,ε,ξε,ξ2,ξ2ε2) (16) γ¯ξδ=γ¯ξδ (1,ξ,ε,ξε,ε2,ξε2)γ¯εδ=γ¯εδ (1,ξ,ε,ξε,ε2,ξε2). (17) The original shear strain obtained from the Lagrange shape functions γ ξδ and γ εδ is γξδ=ζξ+∂w∂ξ=γξδ (1,ξ,ε,ξε,ξ2,ξ2ε,ε2,ξε2,ξ2ε2)γεδ=ζε+∂w∂ε=γεδ (1,ξ,ε,ξε,ξ2,ξ2ε,ε2,ξε2,ξ2ε2).…”

Linear Vibration Analysis of Shells Using a Seven-Parameter Spectral/hp Finite Element Model

“…Kant et al [23] presented a dynamic analysis model by means of degenerated shell elements, where the discretization of the 3D elasticity equations is made in terms of mid-surface nodal variables. In this formulation, five parameters were used to define the shell kinematic; however, they do not present any analysis to determine natural frequencies.…”