Enhanced Beetle Antennae Algorithm for Chemical Dynamic Optimization Problems’ Non-Fixed Points Discrete Solution

Dynamic optimization is an important research topic in chemical process control. A dynamic optimization method with good performance can reduce energy consumption and prompt production efficiency. However, the method of solving the problem is complicated in the establishment of the model, and the process of solving the optimal value has a certain degree of difficulty. Based on this, we proposed a non-fixed points discrete method of an enhanced beetle antennae optimization algorithm (EBSO) to solve this kind of problem. Firstly, we converted individual beetles into groups of beetles to search for the best and increase the diversity of the population. Secondly, we introduced a balanced direction strategy, which explored extreme values in new directions before the beetles updated their positions. Finally, a spiral flight mechanism was introduced to change the situation of the beetles flying straight toward the tentacles to prevent the traditional algorithm from easily falling into a certain local range and not being able to jump out. We applied the enhanced algorithm to four classic chemical problems. Meanwhile, we changed the equal time division method or unequal time division method commonly used to solve chemical dynamic optimization problems, and proposed a new interval distribution method—the non-fixed points discrete method, which can more accurately represent the optimal control trajectory. The comparison and analysis of the simulation test results with other algorithms for solving chemical dynamic optimization problems show that the EBSO algorithm has good performance to a certain extent, which further proves the effectiveness of the EBSO algorithm and has a better optimization ability.

Towards a macroscopically consistent discrete method for granular materials: Delaunay strain-based formulation

We demonstrate that the Delaunay-based strain definition proposed by Bagi (Mech Mater 22:165–177, 1996) for granular media can be straightforwardly translated into a particle-based numerical method for continua. This method has a number of attractive features, including linear completeness and satisfaction of the patch test, exact conservation of linear and angular momenta in the absence of external forces and torques, and anti-symmetry of the gradient vectors for any two points not both on the boundary of the computational domain. The formulation in effect relies on nodal (particle) interpolation of the deformation gradient and is therefore inherently unstable. Drawing on the analogy with granular media, a pairwise interaction between particles is included to alleviate this issue. The underlying idea is to define a local, non-affine deformation of each bond or contact, and to introduce pairwise forces via a stored-energy functional expressed in terms of the corresponding local displacements. In this manner, a generalisation of the Ganzenmüller (Comput Methods Appl Mech Eng 286:87–106, 2015) hourglass stabilisation procedure to non-central forces is obtained. The performance of the method is demonstrated in a range of problems. This work can be considered a first step towards the development of a macroscopically consistent discrete method for granular materials.

Numerical analysis of doubly-history dependent variational inequalities in contact mechanics

This paper is devoted to numerical analysis of doubly-history dependent variational inequalities in contact mechanics. A fully discrete method is introduced for the variational inequalities, in which the doubly-history dependent operator is approximated by repeated left endpoint rule and the spatial variable is approximated by the linear element method. An optimal order error estimate is derived under appropriate solution regularities, and numerical examples illustrate the convergence orders of the method.

Comparison of Calculation Methods of Elastic Bonding: Limits of the Gamma Method Using an Example of a Wood–Concrete Composite Floor with Single Loads

Various methods are available for the calculation of timber–concrete composite floors. The gamma method, which is important in construction practice, as well as the differential equation method, are based on the simplified assumption of a continuous bond between wood and concrete. This makes it possible to analytically calculate the internally statically indeterminate partial section sizes and deformation sizes, analogous to the force size method. In this paper, two typical load situations of concentrated loads (central and off-centre) were analytically and numerically evaluated and compared using the above-mentioned methods (gamma and differential equation), with a discrete method for the case of a timber beam reinforced with a concrete slab using screws as fasteners. The calculation results show significant deviations, which speak for the application of discrete methods in certain load situations and thus limit the usability of the gamma method under certain conditions. For the problem of deflection determination, which is not dealt with in the literature for the discrete method, a numerical method is described in the present work, which was first developed and presented by the first author.

Analysis of Characteristics of Damping Valve Based on High-Order Discrete Scheme

In this paper, based on the high-order discrete scheme, a two-way fluid-solid coupling numerical simulation is for the damping valve plate. According to the discrete method, the governing equations of fluid structure coupling of damping valve plate are studied, including the basic conservation laws; Meanwhile, it analyzes the discretization of the control equation, including the discretization method and the high-order discretization format when the finite volume method is adopted. And based on this discrete format, a numerical simulation was performed on the damping valve, the oil flow condition is analyzed, and the velocity of the throttling hole at different time points and the throttling pressure are analyzed.

Research on Collision Detection Method of Contact On-line Measurement

In order to avoid collision and improve the safety of on-line measurement, a contact on-line measurement collision detection method is studied. Firstly, according to the structural characteristics of the probe and workpiece, the dynamic collision detection between the probe and workpiece is transformed into static collision detection by using the discrete method, and then the grid division of the collision detection space is carried out by using the space division method. Finally, the dynamic collision detection between the probe and workpiece is transformed into the intersection judgment between simple geometry, and according to different collision accuracy requirements, Hierarchical collision detection combining rough detection and fine detection is carried out. Experimental results show that the hierarchical collision detection algorithm has high detection speed and accuracy.

Dynamic Characteristics Analysis of a Circumferential Short Spring Dual Mass Flywheel with the Influence of Centrifugal Force and Friction

Multiple sets of spring, spring seat structures are uniformly arranged in circumferential short spring dual mass flywheel (DMF), which generally have a symmetrical structure. The internal springs and spring seats are constrained by the shape of the primary flywheel and the secondary flywheel. At different rotational speeds, the springs and spring seats have different centrifugal forces. To study the dynamic characteristics of the DMF including torque and stiffness with considering the influence of centrifugal force and friction, the discrete method is used to analyze the mechanical actions of the transmission parts in DMF. The torque action between the spring seat and the secondary flywheel is deduced. The dynamic characteristics of the DMF are obtained through analyzing and calculating. Due to the symmetry of the structure, the torque transmitted and the stiffness of the DMF also have specific symmetrical characteristics. Namely, at two relative rotational angles of the same magnitude and opposite direction, the magnitude of the transmitted torque is the same, the direction is opposite. The magnitude and direction of stiffness are the same. The influence of speed, friction coefficient, spring mass, and spring seat mass on the torque and stiffness characteristics are analyzed. Finally, the theoretical analysis is proved to be valid by the torque characteristics test of DMF.

Serial encryption using the functions of real variable

Context. Using the functions of a real variable in cryptosystems as keys allow increasing their cryptographic strength since it is more difficult to select such keys. Therefore, the development of such systems is relevant. Objective. Cryptosystems with symmetric keys are proposed for encrypting and decrypting a sequence of characters represented as a one-dimensional numerical array of ASCII codes. These keys are functions of a real variable that satisfies certain restrictions. They can be both continuous and discrete. Method. Two cryptosystem options are proposed. In the first embodiment, the transmitting and receiving sides select two functions, the first transmitted symbol, the area of the function definition, and the step of changing the function argument. Discrete messages are encrypted by calculating the first-order integral disproportion of the encrypted array using a function. The corresponding value of the second function is added to the obtained cipher of each symbol for scrambling to complicate the analysis of the intercepted message. On the receiving side, the second function is subtracted and decryption performed by the inverse transformation of the formula for integral disproportion. In the second version, sequential encryption is performed when the cipher obtained using one of the key functions in the first stage is encrypted again by calculating the disproportion using the second function, the key. Accordingly, in two stages, decryption is performed. Results. Examples of encryption and decryption of a sequence of text characters are presented. It is shown that the same character is encoded differently depending on its position in the message. In the given examples it is presented the difficulty of key functions parameters choosing and the cryptographic strength of the proposed cryptosystem. Conclusions. Variants of the cryptosystem using the first-order integral disproportion function are proposed, in which the functions of a real variable serve as keys. To “crack” such a system, it is necessary not only to select the form of each function but also to find the values of its parameters with high accuracy. The system has high cryptographic strength.

Transverse Vibration Analysis of Axially Moving Trapezoidal Plates

Transverse vibration of axially moving trapezoidal plates is investigated. The differential equation of transverse vibration for a axially moving trapezoidal plate is established by D'Alembert principle. The original trapezoid region can be replaced by regular square region by the medium parameter method for the convenience of calculation. A generalized complex eigenvalue equation is derived by a discrete method (the differential quadrature method). The complex frequency curve of trapezoidal plate is obtained by calculating the eigenvalue equation. The change of the complex frequencies of the axially moving trapezoidal plates with the dimensionless axially moving speed is analyzed. The effects of the aspect ratio and the trapezoidal angle on instability type of the trapezoidal plate are discussed under different boundary conditions. The results of numerical analysis show that there are two main instability types of axially moving trapezoidal plate: divergence and flutter. The modal orders of the two types of instability are also different, which is related to the trapezoidal angle, aspect ratio and boundary condition of the trapezoidal plate.