GEOMETRICALLY NONLINEAR STABILITY ANALYSIS OF SHELLS USING GENERALIZED CONFORMING SHALLOW SHELL ELEMENT

2001 ◽  
Vol 01 (03) ◽  
pp. 313-332 ◽  
Author(s):  
JIANHENG SUN ◽  
ZHIFEI LONG ◽  
YUQIU LONG ◽  
CHUNSHENG ZHANG
Keyword(s):  
Degrees Of Freedom ◽  
Shallow Shell ◽  
Shell Element ◽  
Linear Analysis ◽  
Continuity Condition ◽  
Body Motion ◽  
Geometrically Nonlinear ◽  
Nonlinear Stability Analysis ◽  
Plate And Shell ◽  
Element Theory

A generalized conforming finite element theory was presented to satisfy the C1 continuity condition for plate and shell element. The effectiveness of the theory in the linear analysis has been proved. This paper discusses the membrane locking phenomenon of shallow shell element based on the satisfaction of the requirement of rigid body motion, and a technique is developed to eliminate the membrane locking phenomenon. Accordingly a geometrically nonlinear generalized conforming rectangular shallow shell element with tangential degrees of freedom of midpoints of sides is formulated. Nonlinear numerical analysis of shell stability shows that the element exhibits high precision and fast convergence characteristics.

scholarly journals Geometrically nonlinear analysis of thin shell by a quadrilateral finite element with in-plane rotational degrees of freedom

2010 ◽  
pp. 707-724
Author(s):  
Djamel Boutagouga ◽  
Abdelhacine Gouasmia ◽  
Kamel Djeghaba
Keyword(s):  
Nonlinear Analysis ◽  
Thin Shell ◽  
Degrees Of Freedom ◽  
Shell Element ◽  
Local System ◽  
Second Phase ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Rotational Degrees Of Freedom ◽  
Quadrilateral Finite Element

We present in this research article, the improvements that we made to create a four nodes flat quadrilateral shell element for geometrically nonlinear analysis, based on corotational updated lagrangian formulation. These improvements are initially related to the improvement of the in-plane behaviour by incorporation of the in-plane rotational degrees of freedom known as “drilling degrees of freedom” in the membrane displacements field formulation. In the second phase, a co-rotational spatial local system of axes which adapts well to the problems of quadrilateral elements is adopted, while ensuring simplicity and effectiveness at numerical level. The required goal being mainly to have a robust thin shell element associated with a simplified formulation. The obtained element remains economic, and showing a robust behaviour in delicate situations of tests.

scholarly journals A 6-parameter triangular flat shell element for nonlinear analysis

2019 ◽  
pp. 237-268 ◽  
Author(s):  
Professor Mohammad Rezaiee-Pajand ◽  
Amir R. Masoodi ◽  
E. Arabi
Keyword(s):  
Degrees Of Freedom ◽  
Shell Element ◽  
Geometrically Nonlinear ◽  
Nonlinear Analyses ◽  
Six Degrees Of Freedom ◽  
Triangular Shell Element ◽  
Rotation Method ◽  
Flat Shell Element ◽  
Rotational Degrees Of Freedom ◽  
Convergence Study

In this paper, an improved flat triangular shell element is proposed. This element has three nodes, and in each node, six degrees of freedom are considered. Since there are three rotational degrees of freedom at each node, the drilling effect can be incorporated in authors' formulation. A new procedure is also suggested for updating the director vectors about which the rotational degrees of freedom are defined. In order to study large displacements and rotations, Total Lagrangian principles are employed. In addition, updating the rotational degrees of freedom is implemented using enriched updated director vectors, which are formulated based on the finite rotation method. On the other hand, small strains are considered in this formulation. By utilizing MITC method, shear and membrane locking is mitigated from new element. To examine the performance, the element passes three basic tests, including isotropy, and patch test. Moreover, a convergence study is also implemented to show the elemental behavior. Several popular benchmarks are considered to illustrate the accuracy and capability of the suggested element in geometrically nonlinear analyses.    

Numerical Simulation of Multiple Floating Structures With Nonlinear Constraints

2002 ◽  
Vol 124 (2) ◽  
pp. 104-109 ◽  
Author(s):  
Subrata K. Chakrabarti
Keyword(s):  
Degrees Of Freedom ◽  
Order Theory ◽  
Frequency Domain Analysis ◽  
Body Motion ◽  
Single Frequency ◽  
Integration Scheme ◽  
Mooring Lines ◽  
Floating Structures ◽  
Irregular Wave ◽  
Exciting Forces

A versatile and efficient numerical analysis is developed to compute the responses of a moored floating system composed of multiple floating structures. Structures such as tankers, semisubmersibles, FPSOs, SPARs, TLPs, and SPMs connected by mooring lines, connectors or fenders may be analyzed individually or collectively including multiple interaction. The analysis is carried out in the time domain assuming rigid body motion for the structures, and the solution is generated by a forward integration scheme. The analysis includes the nonlinearities in the excitation, damping, and restoring terms encountered in a typical mooring system configuration. It also allows for instabilities in the tower oscillation as well as slack mooring lines. Certain simplifications in the analysis have been made, which are discussed. The exciting forces in the analysis are wind, current, and waves (including a steady and an oscillating drift force), which are not necessarily collinear. The waves can be single frequency or composed of multiple frequency components. For regular waves either linear, stretched linear or fifth order theory may be used. The irregular wave may be included as a given spectral model (e.g., PM or JONSWAP). The vessels are free to respond to the exciting forces in six degrees of freedom—surge, sway, heave, roll, pitch, and yaw. The tower, when present, is free to respond in two degrees of freedom—oscillation and precession. The loads in the mooring lines are determined from prescribed tension-strain tables for the lines. Rigid mooring arms can be analyzed by allowing for compression in the load-strain table. Fenders may be input similarly through load compression tables. In order to establish the stability and accuracy of the solution, comparison of the results with linearized frequency domain analysis was made. The analysis is verified by several different model test results for different structure configurations in regular and random seas. Some of the interesting aspects of nonlinear system are shown with a few examples.

Rolling Condition and Gyroscopic Moments in Curve Negotiations

2012 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Martin B. Hamper ◽  
James J. O’Shea
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Global Coordinate System ◽  
Gyroscopic Moment ◽  
Absolute Angular Velocity ◽  
Pure Rolling ◽  
The Stability

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of changes of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible, and in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion, and therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, The analysis presented in this paper shows that the roll moment which can have a significant effect on the wheel/rail contact forces depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components, and therefore, cannot be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

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