Experimental analysis on mechanical properties of BF/PLA composites and its lightweight design on power battery box

In response to the concept of energy conservation and environmental protection, a novel composite battery box with BF/PLA composite is proposed. Firstly, the mechanical properties of BF/PLA composite are tested, and it is concluded that the property parameters of BF/PLA composite with 50% BF mass fraction is selected as the material property parameter of subsequent finite element simulation. Subsequently, the statics analysis and constraint modal analysis of the traditional metal battery box are carried out under the typical working conditions of rapid turning and braking under vertical bumping. Based on this, the upper and lower box materials of the battery box except the bracket are replaced by BF/PLA composite. The morphology optimization, topology optimization and free size optimization are carried out with the constraint that the first-order modal vibration frequency is no less than 30 Hz. Compared with the traditional metal battery box, the stiffness and strength of the optimized BF/PLA composite battery box are significantly enhanced. Moreover, the first-order constraint modal frequency increases by 15.5%, and the comprehensive weight reduction ratio reaches 40.88%. Finally, the optimized BF/PLA composite battery box is verified under random vibration, mechanical shock analysis, collision analysis, extrusion and falling ball analysis and drop analysis conditions. Meanwhile, compared with the traditional metal battery box under the same working conditions, the excellent reliability of the composite battery box is highlighted. The proposed BF/PLA composite battery box satisfies the requirements of stiffness and strength performances under various working conditions, which provides theoretical and data support for the application of composite materials in battery box and other automotive components.

Second-order efficient optimality conditions for set-valued vector optimization in terms of asymptotic contingent epiderivatives

We propose a generalized second-order asymptotic contingent epiderivative of a set-valued mapping, study its properties, as well as relations to some second-order contingent epiderivatives, and sufficient conditions for its existence. Then, using these epiderivatives, we investigate set-valued optimization problems with generalized inequality constraints. Both second-order necessary conditions and sufficient conditions for optimality of the Karush-Kuhn-Tucker type are established under the second-order constraint qualification. An application to Mond-Weir and Wolfe duality schemes is also presented. Some remarks and examples are provided to illustrate our results.

Philosophical Foundations of the Law of Equity

A late-comer to the field of private law theory, the inquiry into the foundations of the law of Equity raises some fundamental questions about the relationships between law and morality, the nature of rights, the extent to which we are willing to compromise on the Rule of Law ideal in order to achieve various social goals. In this volume, leading scholars in the field address these and the questions about underlying principles of Equity and its relationship to the common law: What relationships, if any, are there between the legal, philosophical, and moral senses of ‘equity’? Does Equity form a second-order constraint on law? If so, is its operation at odds with the rule of law? Do the various theories of Equity require some kind of separation of law and equity—and, if they do, what kind of separation? The volume further sheds light on some of the most topical questions of jurisprudence that are embedded in the debate around ‘fusion’.

Notes on Constraint Qualifications for Second-Order Optimality Conditions

In the first part of this paper we point out some basic properties of the critical cones used in second-order optimality conditions and give a simple proof of a strong second-order necessary optimality condition by assuming a “modified” first-order Abadie constraint qualification. In the second part we give some insights on second-order constraint qualifications related to second-order local approximations of the feasible set.

Quantum Cosmologies Under Geometrical Unification of Gravity and Dark Energy

A Friedmann–Robertson–Walker Universe was studied with a dark energy component represented by a quintessence field. The Lagrangian for this system, hereafter called the Friedmann–Robertson–Walker–quintessence (FRWq) system, was presented. It was shown that the classical Lagrangian reproduces the usual two (second order) dynamical equations for the radius of the Universe and for the quintessence scalar field, as well as a (first order) constraint equation. Our approach naturally unified gravity and dark energy, as it was obtained that the Lagrangian and the equations of motion are those of a relativistic particle moving on a two-dimensional, conformally flat spacetime. The conformal metric factor was related to the dark energy scalar field potential. We proceeded to quantize the system in three different schemes. First, we assumed the Universe was a spinless particle (as it is common in literature), obtaining a quantum theory for a Universe described by the Klein–Gordon equation. Second, we pushed the quantization scheme further, assuming the Universe as a Dirac particle, and therefore constructing its corresponding Dirac and Majorana theories. With the different theories, we calculated the expected values for the scale factor of the Universe. They depend on the type of quantization scheme used. The differences between the Dirac and Majorana schemes are highlighted here. The implications of the different quantization procedures are discussed. Finally, the possible consequences for a multiverse theory of the Dirac and Majorana quantized Universe are briefly considered.