A Finite Element Model for Thick-Walled Axisymmetric Shells

1982 ◽  
Vol 104 (3) ◽  
pp. 215-222 ◽  
Author(s):  
D. J. Barrett ◽  
A. Soler
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Finite Element Model ◽  
Thin Shell ◽  
Element Model ◽  
Order Theory ◽  
Higher Order ◽  
Shells Of Revolution ◽  
Geometric Conditions ◽  
Higher Order Theory

The symmetrically loaded moderately thick-walled shell of revolution can be treated by general finite elements, or for certain geometric conditions, by extended thin shell finite elements that have incorporated transverse shear deformation. In this work, we develop a higher order theory finite element model for symmetrically loaded shells of revolution which is useful for configurations which are out of the range of validity of the extended thin shell elements. Legendre polynomial series expansions are key features of the development and lead to nonlinear distributions of both stress and deformation in the thickness variable. Problems are solved to yield some initial data for comparison of the cost and accuracy of the higher order theory finite element model to other shell element models.

A SPECTRAL/hp NONLINEAR FINITE ELEMENT ANALYSIS OF HIGHER-ORDER BEAM THEORY WITH VISCOELASTICITY

2012 ◽  
Vol 04 (01) ◽  
pp. 1250010 ◽  
Author(s):  
V. P. VALLALA ◽  
G. S. PAYETTE ◽  
J. N. REDDY
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Virtual Work ◽  
Constitutive Relations ◽  
Beam Theory ◽  
Element Model ◽  
Higher Order ◽  
Time Step ◽  
Third Order ◽  
The Third

In this paper, a finite element model for efficient nonlinear analysis of the mechanical response of viscoelastic beams is presented. The principle of virtual work is utilized in conjunction with the third-order beam theory to develop displacement-based, weak-form Galerkin finite element model for both quasi-static and fully-transient analysis. The displacement field is assumed such that the third-order beam theory admits C0 Lagrange interpolation of all dependent variables and the constitutive equation can be that of an isotropic material. Also, higher-order interpolation functions of spectral/hp type are employed to efficiently eliminate numerical locking. The mechanical properties are considered to be linear viscoelastic while the beam may undergo von Kármán nonlinear geometric deformations. The constitutive equations are modeled using Prony exponential series with general n-parameter Kelvin chain as its mechanical analogy for quasi-static cases and a simple two-element Maxwell model for dynamic cases. The fully discretized finite element equations are obtained by approximating the convolution integrals from the viscous part of the constitutive relations using a trapezoidal rule. A two-point recurrence scheme is developed that uses the approximation of relaxation moduli with Prony series. This necessitates the data storage for only the last time step and not for the entire deformation history.

A New Rectangular Plate Element for Vibration Analysis of Laminated Composites

1998 ◽  
Vol 120 (1) ◽  
pp. 80-86 ◽  
Author(s):  
Guan-Liang Qian ◽  
Suong V. Hoa ◽  
Xinran Xiao
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Rectangular Plate ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Element Model ◽  
Higher Order ◽  
Transverse Displacement

In this paper, a higher order rectangular plate bending element based on a Higher Order Shear Deformation Theory (HSDT) is developed. The element has 4 nodes and 20 degrees of freedom. The transverse displacement is interpolated by using an optimized interpolation function while the additional rotation degrees of freedom are approximated by linear Lagrange interpolation. The consistent element mass matrix is used. A damped element is introduced to the finite element model. The proposed FEM is used to calculate eigenfrequencies and modal damping of composite plates with various boundary conditions and different thicknesses. The results show that the present FEM gives excellent results when compared to other methods and experiment results, and is efficient and reliable for both thick and thin plates. The proposed finite element model does not lock in the thin plate situation and does not contain any spurious vibration mode, and converges rapidly. It will provide a good basis for the inverse analysis of vibration of a structure.

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