Continuum Mechanics, Nonlinear Finite Element Techniques and Computational Stability

Author(s):  
P. Wriggers
Author(s):  
Hiroyuki Sugiyama ◽  
Aki M. Mikkola ◽  
Ahmed A. Shabana

In this investigation, a nonlinear finite element method for the large deformation and rotation of cable problems is presented. This method is based on the finite element absolute nodal coordinate formulation that guarantees the continuity of all the displacement gradients and leads to a constant mass matrix. The classical cable theory is first reviewed and the assumptions used in this linear theory are defined in order to demonstrate the basic differences between the linear theory and the nonlinear finite element formulation proposed in this paper for cable applications. The elastic cable forces in the absolute nodal coordinate formulation are obtained in this investigation using a general continuum mechanics approach that accounts for the effect of all geometric nonlinearities. It is shown in this investigation that the use of the general continuum mechanics approach leads to a simpler and more efficient formulation as compared to the use of the assumptions of the linear theory that employs a local finite element coordinate system. The results obtained using the absolute nodal coordinate formulation show a good agreement with the results obtained using the classical cable theory when linear cable problems are considered. The results of this investigation obtained using explicit numerical integration also show the potential of the proposed finite element formulation in the nonlinear analysis of cables that experience large rotations and large deformations. It is also shown that the use of perturbation methods to linearize the finite element equations of motion leads to modal characteristics results that are in a good agreement with the linear theory. The generalization of the procedure presented in this paper to three-dimensional cable problems is demonstrated and the computer implementation in multibody algorithms is discussed.


2003 ◽  
Vol 125 (4) ◽  
pp. 746-756 ◽  
Author(s):  
Hiroyuki Sugiyama ◽  
Aki M. Mikkola ◽  
Ahmed A. Shabana

In this investigation, a nonlinear finite element method for the large deformation and rotation of cable problems is presented. This method is based on finite element absolute nodal coordinate formulation that guarantees the continuity of all displacement gradients and leads to a constant mass matrix. The classical cable theory is first reviewed and the assumptions used in this linear theory are defined in order to demonstrate the basic differences between the linear theory and the nonlinear finite element formulation proposed in this paper for cable applications. The elastic cable forces in the absolute nodal coordinate formulation are obtained using a general continuum mechanics approach that accounts for the effect of all geometric nonlinearities. It is shown in this investigation that the use of the general continuum mechanics approach leads to a simpler and more efficient formulation as compared to the use of the assumptions of the linear theory that employs a local finite element coordinate system. The results obtained using the absolute nodal coordinate formulation show a good agreement with the results obtained using the classical cable theory when linear cable problems are considered. In particular it is shown that the use of perturbation methods to linearize the finite element equations of motion leads to modal characteristics results that are in a good agreement with the linear theory. The results of this investigation obtained using explicit numerical integration also show the potential of the proposed finite element formulation in the nonlinear analysis of cables that experience large rotations and deformations. The generalization of the procedure presented in this paper to three-dimensional cable problems is demonstrated and the computer implementation in multibody algorithms is discussed.


1997 ◽  
Vol 64 (4) ◽  
pp. 835-841 ◽  
Author(s):  
Seung Jo Kim ◽  
Kyeong Su Kim ◽  
Jin Yeon Cho

A viscoelastic model of finitely deforming rubber is proposed and its nonlinear finite element approximation and numerical simulation are carried out. This viscoelastic model based on continuum mechanics is an extended model of Johnson and Quigley’s one-dimensional model. In the extended model, the kinematic configurations and measures based on continuum mechanics are rigorously defined and by using these kinematic measures, constitutive relations are introduced. The obtained highly nonlinear equations are approximated by the nonlinear finite element method, where a mixture of the total and updated Lagrangian descriptions is used. To verify the theory and the computer code, uniaxial stretch tests are simulated for various stretch rates and compared with actual experiments. As a practical example, an axisymmetric rubber plate under various time-dependent pressure loading conditions is analyzed.


Author(s):  
Jing Zhang ◽  
Hong-wei Guo ◽  
Juan Wu ◽  
Zi-ming Kou ◽  
Anders Eriksson

In view of the problems of low accuracy, small rotational angle, and large impact caused by flexure joints during the deployment process, an integrated flexure revolute (FR) joint for folding mechanisms was designed. The design was based on the method of compliance and stiffness ellipsoids, using a compliant dyad building block as its flexible unit. Using the single-point synthesis method, the parameterized model of the flexible unit was established to achieve a reasonable allocation of flexibility in different directions. Based on the single-parameter error analysis, two error models were established to evaluate the designed flexure joint. The rotational stiffness, the translational stiffness, and the maximum rotational angle of the joints were analyzed by nonlinear finite element analyses. The rotational angle of one joint can reach 25.5° in one direction. The rotational angle of the series FR joint can achieve 50° in one direction. Experiments on single and series flexure joints were carried out to verify the correctness of the design and analysis of the flexure joint.


Author(s):  
Furqan Qamar ◽  
Shunde Qin

AbstractAround the globe, the need for additional housing, due to the increase in world population, has led to the exploration of more cost effective and environmentally friendly forms of construction. Out of many technologies found, mortar-free interlocked masonry systems were developed to eliminate the deficiency of traditional masonry. For such systems against earthquakes, lateral resistance can be enhanced with plaster. But there is a need to further improve the performance of plaster in mortar-free interlocking walls for better ductility. The objective of this study is to develop nonlinear finite element (NLFE) models to explore the likely failure mechanism (e.g. bond failure) of such systems and to do parametric studies more cheaply than constructing many walls. Lateral failure load, load–displacement curves and crack patterns were compared with the experimental results. Parametric studies involving variation in block and plaster compressive strength and plaster thickness were undertaken using TNO DIANA NLFE models. A 150% increase in thickness of plaster only resulted in 28% increase in failure load, and column thickness can be reduced to theoretical 25 mm of blocks with 8 mm of plaster and yet exceed the lateral strength of a 150-mm-thick unplastered column. A cost analysis was also carried out, based on NLFE models, and showed that fibrous plastered column with 25-mm-thickness blocks gave equivalent performance to the 150-mm-thick unplastered column with 67% cost saving.


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