scholarly journals Estimated closeness of optimum piecewise constant section width in I-rods with stability or first eigen-frequency limits to the predicted minimum material consumption with regard to strength requirements

2020 ◽  
Vol 22 (4) ◽  
pp. 114-125
Author(s):  
L. S. Lyakhovich ◽  
P. A. Akimov ◽  
B. A. Tukhfatullin
Keyword(s):  
General Problem ◽  
Continuous Change ◽  
Material Consumption ◽  
Piecewise Constant ◽  
Constant Change ◽  
Constant Section ◽  
Eigen Frequency

The previous research described estimated closeness of optimum piecewise constant section width in I-rods with stability or first eigen-frequency limits to the predicted minimum material consumption with regard to strength requirements in continuous change in variable rod parameters. It is however known that in construction, rods are generally designed with piecewise constant change in the section parameters. Besides, in another work, the criterion was formulated for assessment of optimum solutions of piecewise constant sections of I-rods with stability or the first eigen-frequency limits, without considering the strength requirements. This paper focuses on a more general problem of estimated closeness of optimum piecewise constant section width in I-rods with stability or first eigen-frequency limits to the predicted minimum material consumption with regard to strength requirements.

scholarly journals Assessment criterion for optimum design solutions of piecewise constant sections in I-rods with stability or first eigen-frequency limits

2020 ◽  
Vol 22 (3) ◽  
pp. 94-105
Author(s):  
L. S. Lyakhovich ◽  
P. A. Akimov ◽  
B. A. Tukhfatullin
Keyword(s):  
Optimum Design ◽  
Reference Point ◽  
Variable Parameter ◽  
Optimization Methods ◽  
Continuous Change ◽  
Material Consumption ◽  
Assessment Criterion ◽  
Variable Size ◽  
Piecewise Constant ◽  
Eigen Frequency

The criterion for the minimum material consumption of strips strengthening the I-rod with stability or first eigen-frequency limits is formulated in previous studies for the case of continuous change of the variable parameter. It is known that this solution allows evaluating a real design project not only by the criterion of its proximity to the minimum material consumption, but also by the reference point in the real design. In many cases, it is used to replace the continuous change in the variable size of the rod-strengthening piecewise constant sections. The boundaries of these sections are based on the minimum material consumption. The width of the strengthening strips is determined by the optimization methods. The paper proposes the criterion allowing to correctly assess the termination of the optimization processes.

scholarly journals ASSESSMENT CRITERION FOR OPTIMUM DESIGN SOLUTIONS OF PIECEWISE CONSTANT SECTIONS IN RODS OF RECTANGULAR CROSS-SECTION WITH STABILITY OR FIRST EIGEN-FREQUENCY LIMITS

2020 ◽  
Vol 22 (1) ◽  
pp. 75-91
Author(s):  
L. S. Lyakhovich ◽  
P. A. Akimov ◽  
B. A. Tukhfatullin
Keyword(s):  
Optimum Design ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Optimization Methods ◽  
Design Solution ◽  
Material Consumption ◽  
Piecewise Constant ◽  
Stage Process ◽  
Definition Of ◽  
Eigen Frequency

Specific properties of optimum systems have been already considered in previous research. Moreover, the criteria were proposed for a correct assessment of proximity of optimum to minimum material consumption. In particular, the criteria are proposed for rods of rectangular crosssection with stability or first eigen-frequency limits. These criteria can be used for problem optimization, when the rod cross-sections continuously change longitudinally. The obtained optimum solutions can be considered as a perfect limited object. This optimum project function allows researcher to assess the real design solution using the proximity limit criterion (for example, material consumption limit). This kind of optimum design can also be used as a guideline for real design in terms of a stage-by-stage process of transition from a perfect to real object. In this case, it is possible to assess changes in the object optimality at each stage as compared to the initial and idealized solutions. In particular, one of the variants of the process includes replacing the rod with continuous longitudinally varying cross-sections by a rod with piecewise constant sections. The section boundaries can be based on a perfect object, and cross-sections can be determined by one of the optimization methods. This paper presents criteria, which ensure the reliable definition of the time of completion of the optimization process.

scholarly journals ASSESSMENT CRITERIA OF OPTIMAL SOLUTIONS FOR CREATION OF RODS WITH PIECEWISE CONSTANT CROSS-SECTIONS WITH STABILITY CONSTRAINTS OR CONSTRAINTS FOR VALUE OF THE FIRST NATURAL FREQUENCY. PART 1: THEORETICAL FOUNDATIONS

2019 ◽  
Vol 15 (4) ◽  
pp. 88-100 ◽  
Author(s):  
Leonid Lyakhovich ◽  
Pavel Akimov ◽  
Boris Tukhfatullin
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Cross Sections ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Continuous Change ◽  
Material Consumption ◽  
Piecewise Constant ◽  
Ideal Object ◽  
The Cross

The special properties of optimal systems have been already identified. Besides, criteria has been for­mulated to assess the proximity of optimal solutions to the minimal material consumption. In particular, the cri­teria were created for rods with rectangular and I-beam cross-section with stability constraints or constraints for the value of the first natural frequency. These criteria can be used for optimization when the cross sections of a bar change continuously along its length. The resulting optimal solutions can be considered as an idealized ob­ject in the sense of the limit. This function of optimal design allows researcher to assess the actual design solu­tion by the criterion of its proximity to the corresponding limit (for example, regarding material consumption). Such optimal project can also be used as a reference point in real design, for example, implementing a step-by­step process of moving away from the ideal object to the real one. At each stage, it is possible to assess the changes in the optimality index of the object in comparison with both the initial and the idealized solution. One of the variants of such a process is replacing the continuous change in the size of the cross sections of the rod along its length with piecewise constant sections. Boundaries of corresponding intervals can be selected based on an ideal feature, and cross-section dimensions can be determined by one of the optimization methods. The dis­tinctive paper is devoted to criteria that allow researcher providing reliable assessment of the endpoint of the op­timization process.

scholarly journals ASSESSMENT CRITERIA OF OPTIMAL SOLUTIONS FOR CREATION OF RODS WITH PIECEWISE CONSTANT CROSS-SECTIONS WITH STABILITY CONSTRAINTS OR CONSTRAINTS FOR VALUE OF THE FIRST NATURAL FREQUENCY. PART 2: NUMERICAL EXAMPLES

2019 ◽  
Vol 15 (4) ◽  
pp. 101-110 ◽  
Author(s):  
Leonid Lyakhovich ◽  
Pavel Akimov ◽  
Boris Tukhfatullin
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Cross Sections ◽  
Optimal Solutions ◽  
Continuous Change ◽  
Material Consumption ◽  
Piecewise Constant ◽  
Numerical Examples ◽  
Ideal Object ◽  
The Cross

The special properties of optimal systems have been already identified. Besides, criteria has been for­mulated to assess the proximity of optimal solutions to the minimal material consumption. In particular, the cri­teria were created for rods with rectangular and I-beam cross-section with stability constraints or constraints for the value of the first natural frequency. These criteria can be used for optimization when the cross sections of a bar change continuously along its length. The resulting optimal solutions can be considered as an idealized ob­ject in the sense of the limit. This function of optimal design allows researcher to assess the actual design solu­tion by the criterion of its proximity to the corresponding limit (for example, regarding material consumption). Such optimal project can also be used as a reference point in real design, for example, implementing a step-by­step process of moving away from the ideal object to the real one. At each stage, it is possible to assess the changes in the optimality index of the object in comparison with both the initial and the idealized solution. One of the variants of such a process is replacing the continuous change in the size of the cross sections of the rod along its length with piecewise constant sections. Boundaries of corresponding intervals can be selected based on an ideal feature, and cross-section dimensions can be determined by one of the optimization methods. The dis­tinctive paper is devoted to criteria that allow researcher providing reliable assessment of the endpoint of the op­timization process, and the second part of the material presented contains corresponding numerical examples, prepared in accordance with the theoretical foundations given in the first part.

scholarly journals ASSESSMENT CRITERION FOR OPTIMUM DESIGN SOLUTIONS OF PIECEWISE CONSTANT SECTIONS IN RODS OF I-SHAPED CROSS-SECTION WITH STABILITY OR FIRST EIGEN-FREQUENCY LIMITS

2020 ◽  
Vol 22 (1) ◽  
pp. 92-105 ◽  
Author(s):  
L. S. Lyakhovich ◽  
P. A. Akimov ◽  
B. A. Tukhfatullin
Keyword(s):  
Optimum Design ◽  
Cross Sections ◽  
Optimization Methods ◽  
Design Solution ◽  
Material Consumption ◽  
Assessment Criterion ◽  
Piecewise Constant ◽  
Stage Process ◽  
Definition Of ◽  
Eigen Frequency

Specific properties of optimum systems have been already considered in previous research. Moreover, the criteria were proposed for a correct assessment of proximity of optimum to minimum material consumption. In particular, the criteria are proposed for rods of rectangular crosssection with stability or first eigen-frequency limits. These criteria can be used for problem optimization, when the rod cross-sections continuously change longitudinally. The obtained optimum solutions can be considered as a perfect limited object. This optimum project function allows researcher to assess the real design solution using the proximity limit criterion (for example, material consumption limit). This kind of optimum design can also be used as a guideline for real design in terms of a stage-by-stage process of transition from a perfect to real object. In this case, it is possible to assess changes in the object optimality at each stage as compared to the initial and idealized solutions. In particular, one of the variants of the process includes replacing the rod with continuous longitudinally varying cross-sections by a rod with piecewise constant sections. The section boundaries can be based on a perfect object, and cross-sections can be determined by one of the optimization methods. This paper presents criteria, which ensure the reliable definition of the time of completion of the optimization process.

scholarly journals THE SCHEME FOR INVESTIGATION FOR LONGITUDINAL OSCILLATIONS OF ROD OF A PIECEWISE-CONSTANT SECTION

2018 ◽  
pp. 61-70
Author(s):  
R. Tatsij ◽  
O. Chmyr ◽  
O. Karabyn
Keyword(s):  
Software Tools ◽  
Direct Application ◽  
Piecewise Constant ◽  
Graphic Illustration ◽  
Constant Section ◽  
Matrix Calculation

The advantage of this method is a possibility to examine a problem on each breakdown segment and then to combine obtained solutions on the basis of matrix calculation. Such an approach allows the use of software tools for solving the problem and the graphic illustration of the solution. The received results have a direct application to applied problems in the theory of oscillation of the rods with piecewise variables by the distribution of parameters.  

The scheme for investigation for longitudinal oscillations of rod of a piecewise-constant section

2019 ◽  
Vol 2019 (19) ◽  
pp. 149-169
Author(s):  
Oksana Chmyr ◽  
◽  
Oksana Karabyn ◽  
Roman Tatsii ◽  
◽  
...  
Keyword(s):  
Piecewise Constant ◽  
Constant Section

Influence of Magnetic Fields on Solar Hydrodynamics: Experimental Results

1977 ◽  
Vol 36 ◽  
pp. 143-180 ◽  
Author(s):  
J.O. Stenflo
Keyword(s):  
Solar Activity ◽  
Energy Balance ◽  
Magnetic Fields ◽  
Solar Atmosphere ◽  
General Problem ◽  
Solar Rotation ◽  
Active Regions ◽  
Physical Conditions ◽  
Dynamic Phenomena

It is well-known that solar activity is basically caused by the Interaction of magnetic fields with convection and solar rotation, resulting in a great variety of dynamic phenomena, like flares, surges, sunspots, prominences, etc. Many conferences have been devoted to solar activity, including the role of magnetic fields. Similar attention has not been paid to the role of magnetic fields for the overall dynamics and energy balance of the solar atmosphere, related to the general problem of chromospheric and coronal heating. To penetrate this problem we have to focus our attention more on the physical conditions in the ‘quiet’ regions than on the conspicuous phenomena in active regions.

Dynamic low-dose electron diffraction and imaging of phase transitions in polymers

1993 ◽  
Vol 51 ◽  
pp. 890-891
Author(s):  
David C. Martin ◽  
Jun Liao
Keyword(s):  
Crystal Structure ◽  
Phase Transition ◽  
Electron Diffraction ◽  
Low Dose ◽  
Dark Field ◽  
Continuous Change ◽  
Selected Area Electron Diffraction ◽  
Resolution Electron ◽  
Chain Axis ◽  
High Resolution Electron Micrographs

By careful control of the electron beam it is possible to simultaneously induce and observe the phase transformation from monomer to polymer in certain solid-state polymcrizable diacetylenes. The continuous change in the crystal structure from DCHD diacetylene monomer (a=1.76 nm, b=1.36 nm, c=0.455 nm, γ=94 degrees, P2l/c) to polymer (a=1.74 nm, b=1.29 nm, c=0.49 nm, γ=108 degrees, P2l/c) occurs at a characteristic dose (10−4C/cm2) which is five orders of magnitude smaller than the critical end point dose (20 C/cm2). Previously we discussed the progress of this phase transition primarily as observed down the [001] zone (the chain axis direction). Here we report on the associated changes of the dark field (DF) images and selected area electron diffraction (SAED) patterns of the crystals as observed from the side (i.e., in the [hk0] zones).High resolution electron micrographs (HREM), DF images, and SAED patterns were obtained on a JEOL 4000 EX HREM operating at 400 kV.

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