Several families with incomparability and complementarity conditions

2019 ◽  
Vol 266 ◽  
pp. 103-110
Author(s):  
John Goldwasser ◽  
Anthony J.W. Hilton ◽  
Jie Zheng
Keyword(s):  
Complementarity Conditions

scholarly journals Landing Impact Analysis of a Bioinspired Intermittent Hopping Robot with Consideration of Friction

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Long Bai ◽  
Wenjie Ge ◽  
Xiaohong Chen ◽  
Qian Tang ◽  
Rong Xiang
Keyword(s):  
Impact Analysis ◽  
Influence Factors ◽  
Oblique Impact ◽  
Stability Study ◽  
Lessons Learned ◽  
General Applicability ◽  
Complementarity Conditions ◽  
Hopping Robot ◽  
Landing Impact ◽  
The Impact

Multibody dynamics for the flying and landing oblique impact processes of a bioinspired intermittent hopping robot is derived in this paper by using the impulse-momentum principle. The dynamics model that involves the multibody configuration, mass distribution of the robot, and friction is solved by the linear complementarity conditions in terms of different impact types. The computational and experimental data is compared. And the influence factors of landing impact are analysed as well. Based on the influence rules for landing impact, a technical design of solution is proposed for adjusting the robot’s attitude during the jumping and for absorbing the impact energy during the landing. Lessons learned from the theoretical and experimental results have general applicability to the motion prediction, performance analysis, and landing stability study for intermittent hopping robots or other legged robots.

A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Roberto F. Ausas ◽  
Mohammed Jai ◽  
Gustavo C. Buscaglia
Keyword(s):  
Exact Solution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Source Code ◽  
Squeeze Flow ◽  
Complementarity Conditions ◽  
Relaxation Scheme ◽  
Fluid Fraction ◽  
Oscillatory Squeeze Flow

A numerical algorithm for fully dynamical lubrication problems based on the Elrod–Adams formulation of the Reynolds equation with mass-conserving boundary conditions is described. A simple but effective relaxation scheme is used to update the solution maintaining the complementarity conditions on the variables that represent the pressure and fluid fraction. The equations of motion are discretized in time using Newmark’s scheme, and the dynamical variables are updated within the same relaxation process just mentioned. The good behavior of the proposed algorithm is illustrated in two examples: an oscillatory squeeze flow (for which the exact solution is available) and a dynamically loaded journal bearing. This article is accompanied by the ready-to-compile source code with the implementation of the proposed algorithm.

Modeling Contact Dynamics of Vanes With Adjustable Upstream Flow Angles

2012 ◽  
Author(s):  
Daniel Schurzig ◽  
Sebastian Tatzko ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Coulomb Friction ◽  
Nonlinear Behavior ◽  
Simulation Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Dynamics ◽  
Flow Angle ◽  
Complementarity Conditions ◽  
Time Stepping ◽  
Upstream Flow

In this paper, a simulation method is proposed for a sub-category of compressor vanes showing nonlinear behavior due to an adjustable upstream flow angle. The proposed algorithm computes the forced response of a single vane based on the New-mark time stepping scheme after reducing the structural matrices using the Craig-Bampton method. The contacts are modeled by Coulomb friction and Newton impact constraints. Contact forces are determined using linear complementarity conditions with decoupled orthogonal friction force directions. Different discretization methods for the cylindrical contact partners are proposed. Finally, numerical results are shown in order to validate the proposed algorithms.

Small deformation rate-independent plasticity based on a postulate of maximum dissipation

2020 ◽  
pp. 429-433
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Linear Programming ◽  
Plastic Flow ◽  
Yield Surface ◽  
Deformation Rate ◽  
Optimization Problem ◽  
Flow Direction ◽  
Small Deformation ◽  
Complementarity Conditions ◽  
Programming Theory ◽  
Plastic Dissipation

This chapter introduces the concept of maximum dissipation. The elastic set is introduced, and the plastic dissipation is maximized over the elastic set using classical methods from linear programming theory. The plastic flow direction is seen to be generally normal to the yield surface when the plastic dissipation is maximized. The Kuhn-Tucker complementarity conditions are seen in this context to arise from the postulated optimization problem, and the elastic set is seen to be necessarily convex. The concept of maximum dissipation is applied to a Mises material and the models of the earlier chapters are seen to be recovered.

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