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 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 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 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 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 A new hybrid method for size and topology optimization of truss structures using modified ALGA and QPGA

2016 ◽  
Vol 23 (2) ◽  
pp. 252-262 ◽  
Author(s):  
Nima NOII ◽  
Iman AGHAYAN ◽  
Iman HAJIRASOULIHA ◽  
Mehmet Metin KUNT
Keyword(s):  
Cross Sections ◽  
Large Scale ◽  
Convergence Rates ◽  
Design Method ◽  
Optimization Methods ◽  
Cholesky Factorization ◽  
Truss Structures ◽  
Design Solution ◽  
Design Parameters ◽  
Traditional Design

Modified Augmented Lagrangian Genetic Algorithm (ALGA) and Quadratic Penalty Function Genetic Algo­rithm (QPGA) optimization methods are proposed to obtain truss structures with minimum structural weight using both continuous and discrete design variables. To achieve robust solutions, Compressed Sparse Row (CSR) with reordering of Cholesky factorization and Moore Penrose Pseudoinverse are used in case of non-singular and singular stiffness matrix, respectively. The efficiency of the proposed nonlinear optimization methods is demonstrated on several practical exam­ples. The results obtained from the Pratt truss bridge show that the optimum design solution using discrete parameters is 21% lighter than the traditional design with uniform cross sections. Similarly, the results obtained from the 57-bar planar tower truss indicate that the proposed design method using continuous and discrete design parameters can be up to 29% and 9% lighter than traditional design solutions, respectively. Through sensitivity analysis, it is shown that the proposed methodology is robust and leads to significant improvements in convergence rates, which should prove useful in large-scale applications.

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.

Rate Constants, Reactive Flux

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Correlation Function ◽  
Rate Constant ◽  
Cross Sections ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Exact Expression ◽  
Reaction Cross ◽  
Dividing Surface ◽  
Definition Of ◽  
Reactive Flux

This chapter discusses a direct approach to the calculation of the rate constant k(T) that bypasses the detailed state-to-state reaction cross-sections. The method is based on the calculation of the reactive flux across a dividing surface on the potential energy surface. Versions based on classical as well as quantum mechanics are described. The classical version and its relation to Wigner’s variational theorem and recrossings of the dividing surface is discussed. Neglecting recrossings, an approximate result based on the calculation of the classical one-way flux from reactants to products is considered. Recrossings can subsequently be included via a transmission coefficient. An alternative exact expression is formulated based on a canonical average of the flux time-correlation function. It concludes with the quantum mechanical definition of the flux operator and the derivation of a relation between the rate constant and a flux correlation function.

scholarly journals Analysis of the Downscaling Effect and Definition of the Process Fingerprints in Micro Injection of Spiral Geometries

Micromachines ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 335 ◽  
Author(s):  
Antonio Luca ◽  
Oltmann Riemer
Keyword(s):  
Correlation Analysis ◽  
Process Parameters ◽  
Cross Sections ◽  
Mass Production ◽  
Process Window ◽  
Response Variable ◽  
Process Indicators ◽  
Flow Length ◽  
Definition Of ◽  
Microinjection Moulding

Microinjection moulding has been developed to fulfil the needs of mass production of micro components in different fields. A challenge of this technology lies in the downscaling of micro components, which leads to faster solidification of the polymeric material and a narrower process window. Moreover, the small cavity dimensions represent a limit for process monitoring due to the inability to install in-cavity sensors. Therefore, new solutions must be found. In this study, the downscaling effect was investigated by means of three spiral geometries with different cross sections, considering the achievable flow length as a response variable. Process indicators, called “process fingerprints”, were defined to monitor the process in-line. In the first stage, a relationship between the achievable flow length and the process parameters, as well as between the process fingerprints and the process parameters, was established. Subsequently, a correlation analysis was carried out to find the process indicators that are mostly related to the achievable flow length.

scholarly journals Three-dimensional quantification of twisting in the Arabidopsis petiole

2021 ◽  
Author(s):  
Yuta Otsuka ◽  
Hirokazu Tsukaya
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Light Sheet ◽  
Underlying Mechanism ◽  
Two Dimensions ◽  
Observation Angle ◽  
Differential Growth ◽  
Light Sheet Microscopy ◽  
Definition Of ◽  
Twisting Angle

AbstractOrganisms have a variety of three-dimensional (3D) structures that change over time. These changes include twisting, which is 3D deformation that cannot happen in two dimensions. Twisting is linked to important adaptive functions of organs, such as adjusting the orientation of leaves and flowers in plants to align with environmental stimuli (e.g. light, gravity). Despite its importance, the underlying mechanism for twisting remains to be determined, partly because there is no rigorous method for quantifying the twisting of plant organs. Conventional studies have relied on approximate measurements of the twisting angle in 2D, with arbitrary choices of observation angle. Here, we present the first rigorous quantification of the 3D twisting angles of Arabidopsis petioles based on light sheet microscopy. Mathematical separation of bending and twisting with strict definition of petiole cross-sections were implemented; differences in the spatial distribution of bending and twisting were detected via the quantification of angles along the petiole. Based on the measured values, we discuss that minute degrees of differential growth can result in pronounced twisting in petioles.

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