Cities as Solitons: Analytic Solutions to Models of Agglomeration and Related Numerical Approaches

Abstract Direct kinematics with analytic solutions is critical to the real-time control of parallel mechanisms. Therefore, the type synthesis of a mechanism having explicit form of forward kinematics has become a topic of interest. Based on this purpose, this paper deals with the type synthesis of 1T2R parallel mechanisms by investigating the topological structure coupling-reducing of the 3UPS&UP parallel mechanism. With the aid of the theory of mechanism topology, the analysis of the topological characteristics of the 3UPS&UP parallel mechanism is presented, which shows that there are highly coupled motions and constraints amongst the limbs of the mechanism. Three methods for structure coupling-reducing of the 3UPS&UP parallel mechanism are proposed, resulting in eight new types of 1T2R parallel mechanisms with one or zero coupling degree. One obtained parallel mechanism is taken as an example to demonstrate that a mechanism with zero coupling degree has an explicit form for forward kinematics. The process of type synthesis is in the order of permutation and combination; therefore, there are no omissions. This method is also applicable to other configurations, and novel topological structures having simple forward kinematics can be obtained from an original mechanism via this method.

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Singularity analysis and analytic solutions for the Benney–Gjevik equations

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2021-0051 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Andronikos Paliathanasis ◽

Genly Leon ◽

P. G. L. Leach

Keyword(s):

Evolution Equations ◽

Singularity Analysis ◽

Analytic Solutions ◽

Travelling Wave ◽

Travelling Wave Solutions ◽

Painlevé Test ◽

Wave Solutions ◽

Algebraic Solutions

Abstract We apply the Painlevé test for the Benney and the Benney–Gjevik equations, which describe waves in falling liquids. We prove that these two nonlinear 1 + 1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

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Stiffness Estimation and Equivalence of Boundary Conditions in FEM Models

Applied Sciences ◽

10.3390/app11041482 ◽

2021 ◽

Vol 11 (4) ◽

pp. 1482

Author(s):

Róbert Huňady ◽

Pavol Lengvarský ◽

Peter Pavelka ◽

Adam Kaľavský ◽

Jakub Mlotek

Keyword(s):

Boundary Condition ◽

Finite Element ◽

Boundary Conditions ◽

Model Updating ◽

Element Model ◽

Computational Time ◽

Stiffness Coefficients ◽

First Case ◽

Numerical Approaches

The paper deals with methods of equivalence of boundary conditions in finite element models that are based on finite element model updating technique. The proposed methods are based on the determination of the stiffness parameters in the section plate or region, where the boundary condition or the removed part of the model is replaced by the bushing connector. Two methods for determining its elastic properties are described. In the first case, the stiffness coefficients are determined by a series of static finite element analyses that are used to obtain the response of the removed part to the six basic types of loads. The second method is a combination of experimental and numerical approaches. The natural frequencies obtained by the measurement are used in finite element (FE) optimization, in which the response of the model is tuned by changing the stiffness coefficients of the bushing. Both methods provide a good estimate of the stiffness at the region where the model is replaced by an equivalent boundary condition. This increases the accuracy of the numerical model and also saves computational time and capacity due to element reduction.

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