An Investigation of Dynamic Pulse Buckling of Thick Rings

1992 ◽  
Vol 59 (3) ◽  
pp. 615-621 ◽  
Author(s):  
N. G. Pegg
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Numerical Solutions ◽  
Nonlinear Finite Element ◽  
Finite Element Analyses ◽  
Elastoplastic Behavior ◽  
Impulse Load ◽  
Pulse Buckling ◽  
Comparison Of The Results ◽  
Dynamic Pulse

The occurrence of dynamic buckling of thick rings responding to an impulse load is investigated by analytical and numerical solutions to the equation of motion and by nonlinear finite element analyses. An extension to the linearized analytical solution is made using a finite difference scheme which incorporates a nonlinear moment-curvature relationship to model the effects of elastoplastic behavior and strain-rate reversal on the buckle formation. The finite element solution to the problem is formulated with the nonlinear code, ADINA. A comparison of the results shows that the numerical solutions (and, in particular, the ADINA solution) predict a significant reduction in the amplitude of buckling response and an increase in the predominant wavelength of response with time, in comparison to the linear analytical solution. A limited comparison to published experimental results of dynamic pulse buckling of thick rings is also given.

Design of flexure revolute joint based on compliance and stiffness ellipsoids

2021 ◽  
pp. 095441002110169
Author(s):  
Jing Zhang ◽  
Hong-wei Guo ◽  
Juan Wu ◽  
Zi-ming Kou ◽  
Anders Eriksson
Keyword(s):  
Finite Element ◽  
Single Point ◽  
Synthesis Method ◽  
Nonlinear Finite Element ◽  
Finite Element Analyses ◽  
Rotational Stiffness ◽  
Rotational Angle ◽  
Parameterized Model ◽  
Flexure Joints ◽  
Translational Stiffness

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.

Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage

2011 ◽  
Vol 3 (6) ◽  
pp. 729-744
Author(s):  
Zhengzheng Hu ◽  
Mansoor A Haider
Keyword(s):  
Finite Element ◽  
Articular Cartilage ◽  
Analytical Solution ◽  
Conjugate Gradient ◽  
Numerical Solutions ◽  
Elastic Inclusion ◽  
Algebraic Multigrid ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Cpu Time

AbstractIn studying biomechanical deformation in articular cartilage, the presence of cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity problems in which cells are idealized as soft inclusions within a stiff extracellular matrix. An analytical solution of a soft inclusion problem is derived and used to evaluate iterative numerical solutions of the associated linear algebraic system based on discretization via the finite element method, and use of an iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG). Accuracy and efficiency of the AMG-PCG algorithm is compared to two other conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution. While all three algorithms are shown to be accurate, the AMG-PCG algorithm is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased. In contrast to the other two algorithms, the AMG-PCG algorithm also exhibits little sensitivity of CPU time and number of iterations to variations in material properties that are known to significantly affect model variables. Results demonstrate the benefits of algebraic multigrid preconditioners for the iterative solution of assembled linear systems based on finite element modeling of soft elastic inclusion problems and may be particularly advantageous for large scale problems with many nodal unknowns.

scholarly journals Finite Element Analysis of Structural Engineering Problems Using a Viscoplastic Model Incorporating Two Back Stresses

1995 ◽  
Vol 117 (2) ◽  
pp. 377-383 ◽  
Author(s):  
V. K. Arya ◽  
G. R. Halford
Keyword(s):  
Finite Element ◽  
Structural Engineering ◽  
Nonlinear Finite Element ◽  
Finite Element Analyses ◽  
Element Analysis ◽  
Finite Element Program ◽  
Viscoplastic Model ◽  
Engineering Problems ◽  
Element Program ◽  
Viscoplastic Models

The feasibility of a viscoplastic model incorporating two back stresses and a drag strength is investigated for performing nonlinear finite element analyses of structural engineering problems. The model has recently been put forth by Freed and Walker. The feasibility of the viscoplastic model is demonstrated for nonlinear structural analyses by implementing the model into a finite element program and performing nonlinear finite element analyses for several uniaxial and multiaxial problems. Good agreement is shown to exist between the results obtained using the finite element implementation and those obtained experimentally. The advantages of using advanced viscoplastic models for performing nonlinear finite element analyses of structural components are indicated.

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