scholarly journals A mathematical model of transition of the material from elastic to elasto-plastic state

2018 ◽  
Vol 84 (8) ◽  
pp. 55-60
Author(s):  
V. M. Markochev

The goal of this study is to develop a mathematical model of the transition of the structural material from elastic state to elastoplastic state upon tension. The model is based on a modified three-parameter transition operator from one mathematical function to another. A procedure of the mathematical approximation of the transition and corresponding algorithm, which provides a generalized canonical description of the transition, regardless of the form of the functions that characterize the system behavior before and after the transition are presented. The technique is used to describe the transition of two structural materials from the elastic to elastoplastic state upon tension of the samples. Initial sections of the tension diagram are described using three empirical parameters. The role of each of them — maximum permissible relative deformation, transition rate and asymmetry of the transition — are determined. Statistical interpretation of the elastoplastic transition is developed and substantiated. Mathematical expressions for the integral probability function and probability density functions that provide numerical statistical estimation of the degree of change in the state of the structural elements of the material during loading are derived. Analytical description of the initial part of the tension diagram of the material can be used to rearrange the diagrams when modeling deformation processes in conditions of reversible elastoplastic loading.

1989 ◽  
Vol 32 (3) ◽  
pp. 681-687 ◽  
Author(s):  
C. Formby ◽  
B. Albritton ◽  
I. M. Rivera

We describe preliminary attempts to fit a mathematical function to the slow-component eye velocity (SCV) over the time course of caloric-induced nystagmus. Initially, we consider a Weibull equation with three parameters. These parameters are estimated by a least-squares procedure to fit digitized SCV data. We present examples of SCV data and fitted curves to show how adjustments in the parameters of the model affect the fitted curve. The best fitting parameters are presented for curves fit to 120 warm caloric responses. The fitting parameters and the efficacy of the fitted curves are compared before and after the SCV data were smoothed to reduce response variability. We also consider a more flexible four-parameter Weibull equation that, for 98% of the smoothed caloric responses, yields fits that describe the data more precisely than a line through the mean. Finally, we consider advantages and problems in fitting the Weibull function to caloric data.


Author(s):  
Yoshifumi Mori ◽  
Takashi Saito ◽  
Yu Mizobe

We focused on vibration characteristics of reciprocating compressors and constructed the mathematical model to calculate the natural frequencies and modes for crank angles and proposed a method to estimate the degree and the suspicious portion of failure by difference of temporal parameter values obtained using measuring data in operation and the mathematical model. In this paper, according to the proposed method, a case study is carried out using the field data, where the data were acquired before and after the failures occurred in the connecting parts of connecting rod, to prospect the difference between each parameter value for two operating states. Inspecting resonant characteristics each in the frequency response data relating to the natural frequencies for bending modes of the piston rod, we determined two resonant frequencies, which could correspond to the 1st and 2nd mode about bending of the piston rod. To equate the calculated each natural frequency from eigen value analysis based on the proposed model with each resonant frequency, we define the error function for the identified problem, namely optimum problem. In the identified results, it is found that some parameter values have much difference and the corresponding failure could occur around the connecting rod. We could show the possibility to detect both the change of the parameter values and the deterioration parts for two different kinds of the operating states by our proposed method.


2012 ◽  
Vol 19 (2) ◽  
pp. 265-272 ◽  
Author(s):  
N. Gavrilov ◽  
V. Liapidevskii ◽  
K. Gavrilova

Abstract. The evolution of large amplitude internal waves propagating towards the shore and more specifically the run up phase over the "swash" zone is considered. The mathematical model describing the generation, interaction, and decaying of solitary internal waves of the second mode in the interlayer is proposed. The exact solution specifying the shape of solitary waves symmetric with respect to the unperturbed interface is constructed. It is shown that, taking into account the friction on interfaces in the mathematical model, it is possible to describe adequately the change in the phase and amplitude characteristics of two solitary waves moving towards each other before and after their interaction. It is demonstrated that propagation of large amplitude solitary internal waves of depression over a shelf could be simulated in laboratory experiments by internal symmetric solitary waves of the second mode.


2014 ◽  
Vol 716-717 ◽  
pp. 1267-1271
Author(s):  
Liang Jun Yu ◽  
Li Hua Sun ◽  
Cui Cui Huang

Intersymbol Interference (ISI) problem is one of the main factors affecting the baseband transmission performance of mobile communication’s digital signal which can not only reduce the transmission quality of the information but also can result in misinformation and false pass of information and provide troubles to the user and communications. In order to minimize the error rate, we propose a new digital equalization filter and establish the basic model of the digital filter and introduce non-linear Kalman observation equation and the state equation into the model and design partial differential mathematical model of the Kalman filter and develop MATLAB solver based on the mathematical model. In order to verify the validity and reliability of Kalman filter algorithms and mathematical procedures designed in this paper, it uses MATLAB toolbox to simulate the filter of mobile crosstalk signal and obtains amplitude-frequency characteristics and time-domain characteristics before and after filtering. By comparison, we can see that the filter can eliminate the high frequency crosstalk signal which provides technical reference for the study of the problem of crosstalk between the mobile communication codes.


1988 ◽  
Vol 53 (6) ◽  
pp. 1198-1216
Author(s):  
Marie Sýsová ◽  
Ivan Fořt ◽  
Vladimír Kudrna

A mathematical model of the solid particle random motion in a turbulent liquid flow was developed which resulted in an unconventional form of diffusion equation. The diffusion equation derived describes quantitatively the local extremes of the solid phase concentrations in the charge mixed which were verified experimentally. The comparison of the experimental and calculated distribution of local concentrations in the system shows an adequate qualitative agreement. The system consisted of a cylindrical conical-bottomed vessel with baffles and cylindrical draft-tube. A six-blade impeller with inclined (at α = 45° plane blades was used for agitating.


2016 ◽  
Vol 28 (2) ◽  
pp. 197
Author(s):  
R. Carrasco ◽  
J. Singh ◽  
G. P. Adams

Classical studies established that the removal of one of the paired organs produces a compensatory effect on the remaining organ. In the bovine ovary this aspect has not been examined in detail. We took advantage of follicular and luteal profiles from a previous study to retrospectively examine the effects of ovariectomy before and after ovulation on follicular dynamics of the remaining ovary in cattle. To characterise the prevalence and distribution of tyrosine kinase receptor A in the bovine ovary, the original design involved unilateral ovariectomy of cows at different stages of the periovulatory period. For the purposes of the present study, we combined data into 2 groups, a preovulatory group (n = 6 cows) and a post-ovulatory group (n = 5 cows), to provide sufficient data for statistical interpretation. The cows were examined daily by transrectal ultrasonography to determine the ovarian status. For the preovulatory group, a luteolytic dose of prostaglandin was administered when the dominant follicle of the second follicular wave reached ≥10 mm, and the ovary containing the dominant follicle was removed within 48 h. For the post-ovulatory group, ovariectomy was performed on the ovary containing the newly formed corpus luteum between Days 2 to 6 (Day 0 = ovulation). Unilateral ovariectomy was performed by colpotomy under caudal epidural anaesthesia using a chain ecraseur. After ovariectomy, cows were examined daily by ultrasonography from ovariectomy to the completion of an interovulatory interval (period between 2 ovulations). Single-point data were compared between groups by t-test, and binomial data were compared between groups by Fisher’s exact test. Double ovulations were detected in 3/6 ovariectomized in the preovulatory period and 2/5 ovariectomized in the post-ovulatory period. The first ovulation after ovariectomy tended to occur earlier in the preovulatory group than in the post-ovulatory group (P = 0.08), which was attributed primarily to the development of oversized persistent dominant follicles (~20 mm in diameter for ≥7 days in absence of a corpora lutea) in 2 of 5 cows in the post-ovulatory ovariectomy group. The interovulatory interval after ovariectomy was shorter in the post-ovulatory group than in the preovulatory group (14.6 ± 0.3 v. 20.3 ± 0.6 days; P = 0.01). No distinct patterns were detected in follicular and luteal dynamics between the pre- and post-ovulatory ovariectomy groups. The number of follicles ≥3 mm detected by ultrasonography was greater in the post-ovulatory ovariectomy group than in the preovulatory group on Days 6, 7, 8, and 16 of the first interovulatory interval after ovariectomy. In conclusion, results of this retrospective study support the concept that follicular and luteal effects of removal of one ovary are influenced by the timing of ovariectomy relative to ovulation. A prospective study involving a comparison of ovarian dynamics of the same cows before and after unilateral ovariectomy will provide a better understanding of the disruption that take place and the mechanisms controlling it. Research was supported by the Natural Sciences and Engineering Research Council of Canada.


2021 ◽  
Vol 2095 (1) ◽  
pp. 012083
Author(s):  
Zhanxin Li ◽  
Zizhen Cao ◽  
Wenjie Duan ◽  
Yikang Du ◽  
Haiteng Liu

Abstract The most important interfering torque of a three-axis air-bearing simulator is the displacement of the center of mass in the gravity field caused by structural elasticity. In order to characterize the torque, a mathematical model of the interference moment was established. Based on the model, it is suggested that the vertical stiffness and horizontal stiffness of the structure should be equal as far as possible during the structural design, and the elastic unbalance moment can be compensated by the vertical offset of the center of mass of the air floating platform relative to the rotation center after the initial attitude leveling. ABAQUS was used to build a simulation model of the air floating platform, and the changes of the structure’s centroid before and after the gravitational field was applied were extracted by software to simulate the centroid deviation caused by the elastic deformation of the structure, which was used as the characterization to conduct discrete optimization of the structure. The optimal structural parameters were obtained. Then the disturbance torque curve and the corresponding initial centroid offset after initial centroid compensation were calculated by mathematical model. The results are of positive guiding significance to the design of three-axis air-bearing simulator.


2012 ◽  
Vol 12 (1) ◽  
pp. 82
Author(s):  
JAMALUDDIN JAMALUDDIN ◽  
BUDI RAHARDJO ◽  
PUDJI HASTUTI ◽  
ROCHMADI ROCHMADI

Hard and crunchy are specific characteristics of fried product prefered by consumer. To have texture of crunchy productbeing suitable with consumer taste, it is necessary to observ characteristic change of raw material and frying condition. Infrying process, the changes of hardness and crunchiness characteristics of food occur. These changes are predicted caused by free water vaporization and the decrease of starch content in food. The objective of this research is to develop mathematical model of hardness and crunchiness changes as the function of water and extract content degradation. Sample of the research is jack fruit fried in the temperature of 70–100° C, duration of 15–60 minutes, and pressure of 80–90 kPa. The parameters observed are hardness and crunchiness, water and starch content before and after frying. The result showed that hardness and crunciness change as the function of water vaporization and the decrease of starch content can be used to predict hardness and crunciness of product during vacuum frying.


2020 ◽  
Vol 35 ◽  
pp. 04014
Author(s):  
Pavel V. Kruglov ◽  
Alexey G. Ponarin ◽  
Irina A. Bolotina

In modern aerospace technology, one of the perspective ways of assembly parts of thin metal plates is friction stir welding. The advantage of this method is the higher strength of the welds of aluminum alloy joints, compared with the traditional MIG welding for the assembly of rockets and space constructions. However, the lack of friction stir welding is a necessity of formation of the system “machine –tool - part” significantly more effort, which is caused by the need to stir the material in the weld zone in a plastic state. Friction stir welding is used to connect the individual elements of tanks and bodies, in particular, panels, elements of the bottoms with each other. In this paper, is consider the typical design for rocket and space technology bottoms of large tanks. For industrial robot equipped with a special head for friction welding with mixing, a mathematical model of obtaining a spherical bottom from individual segments is proposed. The paper presents a mathematical model describing the geometry of a spherical bottom with a flap articulation and a working zone of an industrial robot, which allows defining constraints on process operation continuous seam welding for standard designs of bottoms and hulls of rocket and space technology. The dependences allowing determining the initial position of the robot relative to the bottom for performing friction stir welding of the continuous seam are proposed.


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