Fast Solution of Transient Elastohydrodynamic Line Contact Problems Using the Trajectory Piecewise Linear Approach

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Daniel Maier ◽  
Corinna Hager ◽  
Hartmut Hetzler ◽  
Nicolas Fillot ◽  
Philippe Vergne ◽  
...  
Keyword(s):  
Piecewise Linear ◽  
Contact Problems ◽  
Galerkin Projection ◽  
Line Contact ◽  
Reduced Order ◽  
Fast Solution ◽  
Speed Up ◽  
Newton Raphson ◽  
First Time ◽  
Piecewise Linear Approach

In order to obtain a fast solution scheme, the trajectory piecewise linear (TPWL) method is applied to the transient elastohydrodynamic (EHD) line contact problem for the first time. TPWL approximates the nonlinearity of a dynamical system by a weighted superposition of reduced linearized systems along specified trajectories. The method is compared to another reduced order model (ROM), based on Galerkin projection, Newton–Raphson scheme and an approximation of the nonlinear reduced system functions. The TPWL model provides further speed-up compared to the Newton–Raphson based method at a high accuracy.

scholarly journals A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion

2021 ◽  
Author(s):  
J. Marconi ◽  
P. Tiso ◽  
D. E. Quadrelli ◽  
F. Braghin
Keyword(s):  
Reduced Order Model ◽  
Galerkin Projection ◽  
Order Model ◽  
Displacement Fields ◽  
Reduced Order ◽  
Total Displacement ◽  
Elastic Forces ◽  
Strain Formulation ◽  
The One ◽  
Definition Of

AbstractWe present an enhanced version of the parametric nonlinear reduced-order model for shape imperfections in structural dynamics we studied in a previous work. In this model, the total displacement is split between the one due to the presence of a shape defect and the one due to the motion of the structure. This allows to expand the two fields independently using different bases. The defected geometry is described by some user-defined displacement fields which can be embedded in the strain formulation. This way, a polynomial function of both the defect field and actual displacement field provides the nonlinear internal elastic forces. The latter can be thus expressed using tensors, and owning the reduction in size of the model given by a Galerkin projection, high simulation speedups can be achieved. We show that the adopted deformation framework, exploiting Neumann expansion in the definition of the strains, leads to better accuracy as compared to the previous work. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.

A Dyad Search Algorithm for Solving Planar Linkages Using the Dyad Method

1992 ◽  
Author(s):  
Lofti Romdhane
Keyword(s):  
Search Algorithm ◽  
Class Ii ◽  
Graph Representation ◽  
Step Size ◽  
Lower Pair ◽  
Fast Solution ◽  
Complete Automation ◽  
Newton Raphson ◽  
Dyad Analysis ◽  
Planar Linkages

Abstract Based on graph representation of planar linkages, a new algorithm was developed to identify the different dyads of a mechanism. A dyad or class II group, is composed of two binary links connected by either a revolute (1) or a slider (0) pair with provision for attachment to other links by lower pair connectors located at the end of each link. There are five types of dyads: the D111, D101, D011, D001, and D010. The dyad analysis of a mechanism is predicated on the ability to construct the system from one or more of the five binary structure groups or class II groups. If the mechanism is complicated and several dyads are involved, the task of identifying these dyads by inspection could be difficult and time consuming for the user. This algorithm allows a complete automation of this task. This algorithm is based on the Dijkstra’s algorithm, for finding the shortest path in a graph, and it is used to develop a computer program, called KAMEL: Kinematic Analysis of MEchanical Linkages, and implemented on an IBM-PC PS/2 model 80. When compared to algorithmic methods, like the Newton-Raphson, the dyad method proved to be a very efficient one and requires as little as one tenth of the time needed by the method using Newton-Raphson algorithm. Moreover, the dyad method yields the exact solution of the position analysis and no initial estimates are needed to start the analysis. This method is also insensitive to the value of the step-size crank rotation, therefore, allowing a very accurate and fast solution of the mechanism at any position of the input link.

Too Popular, Too Fast: Optimal Advertising and Entry Timing in Markets with Peer Influence

2021 ◽  
Author(s):  
Gila E. Fruchter ◽  
Ashutosh Prasad ◽  
Christophe Van den Bulte
Keyword(s):  
Peer Influence ◽  
Boundary Value ◽  
Unknown Boundary ◽  
Entry Costs ◽  
Optimal Advertising ◽  
Fast Solution ◽  
Time Optimal ◽  
Speed Up ◽  
Entry Timing ◽  
Solution Methodology

We study optimal advertising and entry timing decisions for a new product being sold in two-segment markets in which followers are positively influenced by elites, whereas elites are either unaffected or repulsed by product popularity among followers. Key decisions in such markets are not only how much to advertise in each segment over time but also when to enter the follower segment. We develop a continuous-time optimal control model to examine these issues. Analysis yields two sets of two-point boundary value problems where one set has an unknown boundary value condition that satisfies an algebraic equation. A fast solution methodology is proposed. Two main insights emerge. First, the optimal advertising strategy can be U-shaped, that is, decreasing at first to free-ride peer influence but increasing later on to thwart the repulsion influence of overpopularity causing disadoption. Second, in markets where cross-segment repulsion triggers disadoption, advertising is only moderately effective, and entry costs are high, managing both advertising and entry timing can result in significantly higher profits than managing only one of these levers. In markets without disadoption, with high advertising effectiveness or with low entry costs, in contrast, delaying entry may add little value if one already manages advertising optimally. This implies that purveyors of prestige or cool products need not deny followers access to their products in order to protect their profits, and can use advertising to speed up the democratization of consumption profitably. This paper was accepted by Juanjuan Zhang, marketing.

Anisothermal Flow Control by Using Reduced-Order Models

2012 ◽  
Author(s):  
Alexandra Tallet ◽  
Cédric Leblond ◽  
Cyrille Allery
Keyword(s):  
Fluid Flow ◽  
Flow Control ◽  
Projection Method ◽  
Control Strategies ◽  
Pollutant Concentration ◽  
Galerkin Projection ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Optimal Projection ◽  
Fluid Flow Control

Despite constantly improving computer capabilities, classical numerical methods (DNS, LES,…) are still out of reach in fluid flow control strategies. To make this problem tractable almost in real-time, reduced-order models are used here. The spatial basis is obtained by POD (Proper Orthogonal Decomposition), which is the most commonly used technique in fluid mechanics. The advantage of the POD basis is its energetic optimality: few modes contain almost the totality of energy. The ROM is achieved with the recent developed optimal projection [1], unlike classical methods which use Galerkin projection. This projection method is based on the minimization of the residual equations in order to have a stabilizing effect. It enables moreover to access pressure field. Here, the projection method is slightly different from [1]: a formulation without the Poisson equation is proposed and developed. Then, the ROM obtained by optimal projection is introduced within an optimal control loop. The flow control strategy is illustrated on an isothermal square lid-driven cavity and an anisothermal square ventilated cavity. The aim is to reach a target temperature (or target pollutant concentration) in the cavity, with an interior initial temperature (or initial pollutant concentration), by adjusting the inlet fluid flow rate.

An Indirect Boundary Element Formulation for the Solution of Coupled 2D Contact Problems

2009 ◽  
Author(s):  
Angelos Zografos ◽  
Daniele Dini
Keyword(s):  
Boundary Element ◽  
Large Deformations ◽  
Frictional Contact ◽  
Contact Problems ◽  
Element Formulation ◽  
Contact Algorithm ◽  
Subsurface Cracks ◽  
Finite Body ◽  
Material Mismatch ◽  
First Time

An indirect boundary element scheme is employed for the first time to solve two-dimensional, frictional contact problems in the presence of coupling between normal and tangential tractions due to material mismatch and/or geometrical characteristics of the problem under investigation. A fully incremental contact algorithm is used which accounts for changes in the contact regime and the deformed shape of the bodies. The developed algorithm is first validated against the analytical solution obtained for a rigid flat and rounded tilted punch indenting an elastic finite body. The extension of the formulation to treat surface and subsurface cracks, wear and large deformations is also discussed.

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