scholarly journals ASSESSMENT OF THE PROXIMITY OF DESIGN TO MINIMUM MATERIAL CAPACITY SOLUTION OF PROBLEM OF OPTIMIZATION OF THE FLANGE WIDTH OF I-SHAPED CROSS-SECTION RODS WITH ALLOWANCE FOR STABILITY CONSTRAINTS OR CONSTRAINTS FOR THE VALUE OF THE FIRST NATIONAL FREQUE

2020 ◽  
Vol 16 (2) ◽  
pp. 71-82 ◽  
Author(s):  
Leonid Lyakhovich ◽  
Pavel Akimov ◽  
Boris Tukhfatullin
Keyword(s):  
Objective Function ◽  
Natural Frequency ◽  
Cross Section ◽  
Wall Thickness ◽  
Optimal Solution ◽  
Computational Process ◽  
Flange Thickness ◽  
The Cross ◽  
Special Approach ◽  
Shaped Cross Section

There are known methods for optimizing the flange width of I-shaped cross-section rods with stability constraints or the constraints for the value of the first natural frequency. Corresponding objective function has the form of the volume of the flange material for the case when only the flange width varies and the cross-section height, wall thickness and flange thickness are specified. Special criterion for assessment of proximity of corresponding an optimal solution to the design of minimal material capacity was formulated for the considering problem. In this case, the resulting solution may not meet some other unaccounted constraints, for example, strength requirements. Modification of solution in order to meet previously unaccounted constraints does not allow researcher to consider such design as optimal. In the distinctive paper allowance for strength requirements, stability constraints or constraints for the value of the first natural frequency are proposed within considering problem of optimization. Special approach is formulated, which proposes to assess proximity to the design of minimum of material capacity obtained as a result of optimization. Increment of the objective function and criteria corresponding to constrains and restrictions are under consideration within computational process.

scholarly journals Optimization of the cross-sectional shape of the belts of trihedral lattice supports

2019 ◽  
Vol 7 (4) ◽  
pp. 5-8
Author(s):  
Linar Sabitov ◽  
Ilnar Baderddinov ◽  
Anton Chepurnenko
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Cross Section ◽  
Optimization Methods ◽  
Cross Sectional ◽  
Maximum Value ◽  
Axial Moment ◽  
The Cross ◽  
Nonlinear Optimization Methods ◽  
Sectional Shape

The article considers the problem of optimizing the geometric parameters of the cross section of the belts of a trihedral lattice support in the shape of a pentagon. The axial moment of inertia is taken as the objective function. Relations are found between the dimensions of the pentagonal cross section at which the objective function takes the maximum value. We introduce restrictions on the constancy of the consumption of material, as well as the condition of equal stability. The solution is performed using nonlinear optimization methods in the Matlab environment.

scholarly journals CRITERION OF MINIMUMMATERIAL CONSUMPTIONOF FLANGE OF I-SHAPED BAR WITH A VARIATION IN ITS THICKNESS ANDOUTLINE OF THE WIDTH, WITH RESTRICTION TO THE VALUE OF THE CRITICALFORCE OR RESTRICTIONTO THE VALUE OF THEFIRSTNATURAL FREQUENCY INTWO PRINCIPAL PLANESO

2018 ◽  
Vol 14 (2) ◽  
pp. 96-108
Author(s):  
Leonid S. Lyakhovich ◽  
Pavel A. Akimov ◽  
Boris A. Tukhfatullin
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Critical Force ◽  
Principal Plane ◽  
Material Consumption ◽  
The Cross ◽  
The Stability

We have already presented original criterion of minimum material consumption within the design of the outline of the width of the I-shaped bar and the stability constraints or restriction to the value of the first natu­ral frequency in one principal plane of inertia of the cross-section. This paper is devoted in its turn to a criterion for the minimum material capacity of the I-shaped bar with a variation in its thickness and outline of the width, with restrictions to the value of the critical force or restriction to the value of the first natural frequency in two principal planes of inertia of the section

scholarly journals The Cross Sections of Glaciated Valleys

1947 ◽  
Vol 1 (1) ◽  
pp. 37-38 ◽  
Author(s):  
W. V. Lewis
Keyword(s):  
Climatic Change ◽  
Cross Section ◽  
Cross Sections ◽  
River Valley ◽  
Freezing And Thawing ◽  
Melt Water ◽  
The Cross ◽  
Shaped Cross Section

The typical U-shaped cross-section of glaciated valleys is well known but little understood. If a climatic change results in a glacier occupying a deep river valley, and some erosion is assumed to occur wherever the ice makes contact with the bedrock, then a partial change from the “V” to “U” section is to be expected. A more potent agency in such a change is probably the sapping of the valley sides by the alternate freezing and thawing of melt-water flowing down to, and under, the glacier. This has been briefly suggested by de Martonne and worked out somewhat more fully in the case of cirques1

scholarly journals Effective shaping of a bisymmetrical cross section of beams under shear stresses constraints

2021 ◽  
Vol 1199 (1) ◽  
pp. 012062
Author(s):  
K Magnucki ◽  
D Witkowski
Keyword(s):  
Objective Function ◽  
Cross Section ◽  
Analytical Study ◽  
Shear Stresses ◽  
Constraint Condition ◽  
Inertia Moment ◽  
The Subject ◽  
The Cross

Abstract The subject of the studies is effective shaping of an analytically defined, bisymmetrical cross section of beams. The objective function concerns the maximum of the inertia moment and minimum of the area of the cross section. The constraint condition takes into account the maximum shear stresses. The effective shapes of the exemplary beams are derived. Results of the analytical study are presented in Tables and Figures.

Experimental Study on Residual Cross-Sectional Flattening of Thin-Walled Pipes Under Pure Plastic Bending

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Ziqian Zhang
Keyword(s):  
Cross Section ◽  
Wall Thickness ◽  
Residual Deformation ◽  
Outer Diameter ◽  
Cross Sectional ◽  
Plastic Bending ◽  
Thin Walled Pipe ◽  
Bending Radius ◽  
Thin Walled ◽  
The Cross

Abstract Cross-sectional ovalization (ovalization) usually occurs when thin-walled pipe is subjected to large plastic bending. This paper is concerned with residual deformation of thin-walled pipe's cross section in a radial direction when external bending moment is removed. In order to clarify the fundamental ovalization characteristics, find out what factors influence the residual flattening (value of ovalization), the ovalization behavior is investigated experimentally. The experiments are carried out on 21 stainless steel specimens with different geometric parameters under different bending radii by means of a four-point pure bending device. The residual cross-sectional flattenings are monitored continuously by scanning the cross section periodically along the circumferential direction. From the experimental results, it is observed that the cross-sectional shape of the thin-walled pipe is not perfect standard ellipse, and the appearance of the maximum residual flattening is usually found in the direction normal to the neutral surface. It is also revealed the relationships between the residual flattening and the bending radius, the wall thickness, and the pipe outer diameter, i.e., the residual flattening increases as the bending radius and the wall thickness reduce, but it increases as the outer diameter increases. These results are expected to find their potential application in thin-walled pipe bending operation.

The Cross Sections of Glaciated Valleys

1947 ◽  
Vol 1 (01) ◽  
pp. 37-38 ◽  
Author(s):  
W. V. Lewis
Keyword(s):  
Climatic Change ◽  
Cross Section ◽  
Cross Sections ◽  
River Valley ◽  
Freezing And Thawing ◽  
Melt Water ◽  
The Cross ◽  
Shaped Cross Section

The typical U-shaped cross-section of glaciated valleys is well known but little understood. If a climatic change results in a glacier occupying a deep river valley, and some erosion is assumed to occur wherever the ice makes contact with the bedrock, then a partial change from the “V” to “U” section is to be expected. A more potent agency in such a change is probably the sapping of the valley sides by the alternate freezing and thawing of melt-water flowing down to, and under, the glacier. This has been briefly suggested by de Martonne and worked out somewhat more fully in the case of cirques 1

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 Optimization of concurrently compressed and torqued rod

2021 ◽  
Author(s):  
Vladimir Kobelev
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Optimal Solution ◽  
Actual Problem ◽  
Simultaneous Torsion ◽  
Transcendental Functions ◽  
The Cross ◽  
The Stability ◽  
Maximal Moment ◽  
Simply Connected

Abstract The applications of this method for stability problems in the context of twisted and compressed rods are demonstrated in this manuscript. The complement for Euler’s buckling problem is Greenhill's problem, which studies the forming of a loop in an elastic bar under simultaneous torsion and compression (Greenhill, 1883). We search the optimal distribution of bending flexure along the axis of the rod. For the solution of the actual problem the stability equations take into account all possible convex, simply connected shapes of the cross-section. We study the cross-sections with equal principle moments of inertia. The cross-sections are similar geometric figures related by a homothetic transformation with respect to a homothetic center on the axis of the rod and vary along its axis. The cross section that delivers the maximum or the minimum for the critical eigenvalue must be determined among all convex, simply connected domains. The optimal form of the cross-section is known to be an equilateral triangle. The distribution of material along the length of a twisted and compressed rod is optimized so that the rod must support the maximal moment without spatial buckling, presuming its volume remains constant among all admissible rods. The static Euler’s approach is applicable for simply supported rod (hinged), twisted by the conservative moment and axial compressing force. For determining the optimal solution, we directly compare the twisted rods with the different lengths and cross-sections using the invariant factors. The solution of optimization problem for simultaneously twisted and compressed rod is stated in closed form in terms of the higher transcendental functions.

scholarly journals Influencing Variables of Drawing Process using Magnesium Tubes

2019 ◽  
Vol 9 (2) ◽  
pp. 598-601
Keyword(s):  
Cross Section ◽  
Wall Thickness ◽  
Tube Wall ◽  
Drawing Process ◽  
Spring Back ◽  
Bending Angle ◽  
Tube Wall Thickness ◽  
The Cross ◽  
Back Angle ◽  
Thinning Rate

The present work examines the deformation of magnesium tubes using drawing process. During examination, absence of wrinkling and cracking is witnessed at 303k. The effect of mandrel on the cross section of the extruded tubes, wall thickness and spring-back of the bent tube are vividly discussed. Results show that presence of mandrel decreases the cross section of distortion and the spring back angle. Further, the present investigation clarifies the thinning rate of tube wall thickness. It is found that at the bending angle of 90° largest distortion is witnessed.

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