scholarly journals A Sharp Minimum Principle for the Problem of Torsional Rigidity

1999 ◽  
Vol 233 (1) ◽  
pp. 257-265 ◽  
Author(s):  
Xi-nan Ma
Keyword(s):  
Torsional Rigidity ◽  
Minimum Principle ◽  
Sharp Minimum

Constrained Buckling of Spatial Elastica: Application of Optimal Control Method

2018 ◽  
Vol 85 (8) ◽  
Author(s):  
Anna Liakou
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Torsional Rigidity ◽  
Minimum Principle ◽  
Necessary Optimality Conditions ◽  
Buckling Analysis ◽  
Variable Length ◽  
Special Treatment ◽  
Unilateral Constraints ◽  
Constant Length

A post-buckling analysis of a constant or variable length spatial elastica constrained by a cylindrical wall is performed for a first time by adopting an optimal control methodology. Its application in a constrained buckling analysis is shown to be superior when compared to other numerical techniques, as the inclusion of the unilateral constraints is feasible without the need of any special treatment or approximation. Furthermore, the formulation is simple and the optimal configurations of the spatial elastica can be also obtained by considering the minimization condition of the Hamiltonian. We first present the optimal control formulation for the constrained buckling problem of a constant length spatial elastica, including its associated necessary optimality conditions that constitute the Pontryagin's minimum principle. This fundamental constrained buckling problem is used to validate the proposed methodology. The general buckling problem of a variable length spatial elastica is then analyzed that consists of two parts; (1) the solution of the optimal control problem that involves the inserted elastica inside the conduit and (2) the derivation of the buckling load by taking into account the generation of the configurational or Eshelby-like force at the insertion point of the sliding sleeve. A variety of examples are accordingly presented, where the effects of factors, such as the presence of uniform pressure, the clearance of the wall, and the torsional rigidity, on the buckling response of the spatial elastica, are investigated.

The build of nonlinear quantum mechancs and variations of feature of microscopic particles as well as their experimental affirmation

2014 ◽  
Vol 5 (3) ◽  
pp. 871-981 ◽  
Author(s):  
Pang Xiao Feng
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Lagrange Equation ◽  
Minimum Principle ◽  
Superposition Principle ◽  
Type Equation ◽  
Experimental Results ◽  
Traditional Concept ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

We establish the nonlinear quantum mechanics due to difficulties and problems of original quantum mechanics, in which microscopic particles have only a wave feature, not corpuscle feature, which are completely not consistent with experimental results and traditional concept of particle. In this theory the microscopic particles are no longer a wave, but localized and have a wave-corpuscle duality, which are represented by the following facts, the solutions of dynamic equation describing the particles have a wave-corpuscle duality, namely it consists of a mass center with constant size and carrier wave, is localized and stable and has a determinant mass, momentum and energy, which obey also generally conservation laws of motion, their motions meet both the Hamilton equation, Euler-Lagrange equation and Newton-type equation, their collision satisfies also the classical rule of collision of macroscopic particles, the uncertainty of their position and momentum is denoted by the minimum principle of uncertainty. Meanwhile the microscopic particles in this theory can both propagate in solitary wave with certain frequency and amplitude and generate reflection and transmission at the interfaces, thus they have also a wave feature, which but are different from linear and KdV solitary wave’s. Therefore the nonlinear quantum mechanics changes thoroughly the natures of microscopic particles due to the nonlinear interactions. In this investigation we gave systematically and completely the distinctions and variations between linear and nonlinear quantum mechanics, including the significances and representations of wave function and mechanical quantities, superposition principle of wave function, property of microscopic particle, eigenvalue problem, uncertainty relation and the methods solving the dynamic equations, from which we found nonlinear quantum mechanics is fully new and different from linear quantum mechanics. Finally, we verify further the correctness of properties of microscopic particles described by nonlinear quantum mechanics using the experimental results of light soliton in fiber and water soliton, which are described by same nonlinear Schrödinger equation. Thus we affirm that nonlinear quantum mechanics is correct and useful, it can be used to study the real properties of microscopic particles in physical systems.

CHASSIS TORSIONAL RIGIDITY: VALIDATION OF FEA DATA BY EXPERIMENTAL TEST

2019 ◽  
Author(s):  
Luís Fernando Marzola da Cunha ◽  
Matheus Lisboa Cardoch Valdes ◽  
Rhander Viana ◽  
Danilo dos Santos Oliveira ◽  
Luiz Eduardo Rodrigues Vieira
Keyword(s):  
Experimental Test ◽  
Torsional Rigidity

scholarly journals Analytical solution for torsion of cylindrical orthotropic annular wedge-shaped bars reinforced by thin shells

2021 ◽  
Author(s):  
István Ecsedi ◽  
Attila Baksa
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Analytical Method ◽  
Torsional Rigidity ◽  
Circular Ring ◽  
Thin Shells ◽  
Elastic Wedge ◽  
Curved Boundary ◽  
Cylindrically Orthotropic ◽  
Boundary Surfaces

AbstractThis paper deals with the Saint-Venant torsion of elastic, cylindrically orthotropic bar whose cross section is a sector of a circular ring shaped bar. The cylindrically orthotropic homogeneous elastic wedge-shaped bar strengthened by on its curved boundary surfaces by thin isotropic elastic shells. An analytical method is presented to obtain the Prandtl’s stress function, torsion function, torsional rigidity and shearing stresses. A numerical example illustrates the application of the developed analytical method.

scholarly journals A Component-Sizing Methodology for a Hybrid Electric Vehicle Using an Optimization Algorithm

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3147
Author(s):  
Kiyoung Kim ◽  
Namdoo Kim ◽  
Jongryeol Jeong ◽  
Sunghwan Min ◽  
Horim Yang ◽  
...  
Keyword(s):  
Energy Efficiency ◽  
Electric Vehicle ◽  
Optimization Algorithm ◽  
Hybrid Electric Vehicle ◽  
New Technologies ◽  
New Technology ◽  
Dynamic Performance ◽  
Minimum Principle ◽  
Component Sizing ◽  
Hybrid Electric

Many leading companies in the automotive industry have been putting tremendous effort into developing new powertrains and technologies to make their products more energy efficient. Evaluating the fuel economy benefit of a new technology in specific powertrain systems is straightforward; and, in an early concept phase, obtaining a projection of energy efficiency benefits from new technologies is extremely useful. However, when carmakers consider new technology or powertrain configurations, they must deal with a trade-off problem involving factors such as energy efficiency and performance, because of the complexities of sizing a vehicle’s powertrain components, which directly affect its energy efficiency and dynamic performance. As powertrains of modern vehicles become more complicated, even more effort is required to design the size of each component. This study presents a component-sizing process based on the forward-looking vehicle simulator “Autonomie” and the optimization algorithm “POUNDERS”; the supervisory control strategy based on Pontryagin’s Minimum Principle (PMP) assures sufficient computational system efficiency. We tested the process by applying it to a single power-split hybrid electric vehicle to determine optimal values of gear ratios and each component size, where we defined the optimization problem as minimizing energy consumption when the vehicle’s dynamic performance is given as a performance constraint. The suggested sizing process will be helpful in determining optimal component sizes for vehicle powertrain to maximize fuel efficiency while dynamic performance is satisfied. Indeed, this process does not require the engineer’s intuition or rules based on heuristics required in the rule-based process.

scholarly journals An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

2021 ◽  
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande
Keyword(s):  
Optimization Problem ◽  
Volume Fraction ◽  
Minimum Principle ◽  
Equivalent Stress ◽  
Micromechanical Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Pontryagin Minimum Principle ◽  
Volume Fractions ◽  
Material Tailoring

AbstractOne of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

scholarly journals Numerical simulation of the laws of fracture propagation of multi-hole linear co-directional hydraulic fracturing

2021 ◽  
pp. 014459872198899
Author(s):  
Weiyong Lu ◽  
Changchun He
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Minimum Principle ◽  
Fracture Propagation ◽  
Axial Direction ◽  
Rock Breaking ◽  
Hydraulic Fractures ◽  
Directional Hydraulic Fracturing ◽  
Fracture Intersection ◽  
Expansion Stage

Directional rupture is one of the most important and most common problems related to rock breaking. The goal of directional rock breaking can be effectively achieved via multi-hole linear co-directional hydraulic fracturing. In this paper, the XSite software was utilized to verify the experimental results of multi-hole linear co-directional hydraulic fracturing., and its basic law is studied. The results indicate that the process of multi-hole linear co-directional hydraulic fracturing can be divided into four stages: water injection boost, hydraulic fracture initiation, and the unstable and stable propagation of hydraulic fracture. The stable expansion stage lasts longer and produces more microcracks than the unstable expansion stage. Due to the existence of the borehole-sealing device, the three-dimensional hydraulic fracture first initiates and expands along the axial direction in the bare borehole section, then extends along the axial direction in the non-bare hole section and finally expands along the axial direction in the rock mass without the borehole. The network formed by hydraulic fracture in rock is not a pure plane, but rather a curved spatial surface. The curved spatial surface passes through both the centre of the borehole and the axial direction relative to the borehole. Due to the boundary effect, the curved spatial surface goes toward the plane in which the maximum principal stress occurs. The local ground stress field is changed due to the initiation and propagation of hydraulic fractures. The propagation direction of the fractures between the fracturing boreholes will be deflected. A fracture propagation pressure that is greater than the minimum principle stress and a tension field that is induced in the leading edge of the fracture end, will aid to fracture intersection; as a result, the possibility of connecting the boreholes will increase.

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