scholarly journals Topological optimization of the plate

2020 ◽  
pp. 112-119
Author(s):  
Valery Shmukler ◽  
Olena Lugchenko ◽  
Ali Nazhem
Keyword(s):  
Numerical Solutions ◽  
Limit State ◽  
Computational Procedure ◽  
Topological Optimization ◽  
Power Structures ◽  
Plate Design ◽  
New Energy ◽  
Forward Engineering ◽  
New Criterion ◽  
The Given

The paper provides the procedure of forward-engineering (intelligent) plate design. This technology is an exclusive modification of topological (bionic) optimization. It is based on the new energy principles and the algorithms for successive construction of geometric and/or physical-mechanical “pattern” of a structure. The sequence of computational operations of the method in question is illustrated on example of forming plate of energetically uniform strength.   The solution is built analytically to show the nuances of the operations required. The decision of the future analytically helps to show the nuances of the necessary operations. At the same time, on the given supports, it is shown that the introduced optimization criteria determine, at the same time together, the minimum volume of constructs, and also their minimum deflections. A fundamental element of the given approach is the use of a new criterion for the limit state, which provides an estimate of the element’s stress. In this case, the properties of the material and the type of the stress and strain state are taken into account. The analytical solution obtained was used as a checkup test for the general computational procedure of the method in question. In this connection, the paper features the results of analytical and numerical solutions. The efficiency of the computational procedure is confirmed by the rate of its convergence and the minimal variation of geometrical construction parameters (topology) with test cases. The technological sequence of computational operations of the method in question is completed by the construction of elements (plate) with basic external and complex internal geometry, which provides a holistic set of positive power structures, such as minimum consumables in a fixed brutal state, or maximum weight in a fixed organization.

scholarly journals IMPROVEMENT OF CROSS SECTION OF COMPRESSED ELEMENTS BY TOPOLOGICAL RATIONALIZATION

2020 ◽  
Vol 4 (157) ◽  
pp. 25-31
Author(s):  
V. Shmukler ◽  
O. Lugchenko ◽  
A. Nazhem
Keyword(s):  
Cross Section ◽  
Rational Design ◽  
Limit State ◽  
Computational Procedure ◽  
Retaining Walls ◽  
Deformation Energy ◽  
Minimum Volume ◽  
New Energy ◽  
New Criterion ◽  
Energy Principles

The article describes the procedure of direct (rational) design of vertical compressed elements (columns, pylons, stiffening diaphragms, retaining walls). This technology is an exclusive modification of topological (bionic) rationalization. It is based on new energy principles and algorithms for sequential construction of geometric and / or physical-mechanical "image" of the structure. The example of the formation of energy-equivalent columns shows the sequence of computational operations of the method. The solution is built analytically in order to show the nuances of the necessary operations. At the same time, these examples show that the introduced optimization criteria in the form of en → const and U → inf U (here en is the value of the normalized density of potential deformation energy, and U is the potential energy of deformation) determine, including the minimum volume of constructs, as well as their minimum deflections. A fundamental element of the approach is the use of a new criterion of the limit state, which provides an estimate of the intensity of the element. In this case, the properties of the material and the type of stress-strain state are taken into account. The obtained analytical solution was used as a control test for the general computational procedure of the method. In this regard, the article presents the results of the analytical and numerical solution. The efficiency of the computational procedure is confirmed by the speed of its convergence and the minimum difference of geometric parameters (topology) of the structure with test examples. The technological sequence of computational operations of the method is completed by the construction of elements (pylons) with a simple external and complex internal geometry. Keywords: deformation, energy, iteration, voids, cavity, rationalization.

Comparative Analysis, Tools, and Questions

2018 ◽  
Author(s):  
Kathleen Araújo
Keyword(s):  
Comparative Analysis ◽  
Human Development Index ◽  
Energy System ◽  
Home Market ◽  
Energy Technologies ◽  
Energy Transitions ◽  
New Energy ◽  
Quality Of Living ◽  
The Given

This chapter returns to the overarching questions of this book, namely, how can national energy transitions be explained, to what extent do patterns of change align and differ in the transitions of this study, and how does policy play a role, particularly with innovations that emerged amid the transitions. To broadly answer, the four cases are comparatively examined here. The conceptual tools from Chapter 3 are also elaborated based on the findings. Implications of the results are discussed, and will serve as a basis for further discussion in Chapter 9 on how to think about energy transitions as a planner, decision-maker, and researcher. Among the more significant findings are the following. Greater energy substitution (in relative terms) occurred initially within the countries that extended or repurposed existing energy systems versus the country (i.e., Denmark) that developed a new energy system from a nearly non-existent one. Cost improvements were evident in all cases; however, a number of caveats are worth noting. Among the energy technologies and their services that were studied, only Icelandic geothermal-based heating was competitive in its home market in the 1970s; nonetheless, the remaining energy technologies that were studied later became cost competitive. As the national industries of this book became globally recognized, increases in the quality of living within the given countries also occurred, as gauged by the Human Development Index (HDI). With respect to timescales, substantial energy transitions were evident in all cases within a period of 15 years or less. In terms of technology complexity, this attribute was not a confounding barrier to change. Finally, government was instrumental to change, but not always the driver. There are countless ways to compare national energy transitions. This section illustrates ways of doing so, first by describing broadly observed, socio-technical patterns with the tool typologies outlined in Chapter 3. A discussion of tool refinement follows. The section then turns to more systematically assess key, qualitative and quantitative dimensions of the four transition cases.

scholarly journals Numerical Solutions for Multi-Term Fractional Order Differential Equations with Fractional Taylor Operational Matrix of Fractional Integration

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 96 ◽  
Author(s):  
İbrahim Avcı ◽  
Nazim I. Mahmudov
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Main Idea ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Fractional Order Differential Equations ◽  
Fractional Differential ◽  
The Given

In this article, we propose a numerical method based on the fractional Taylor vector for solving multi-term fractional differential equations. The main idea of this method is to reduce the given problems to a set of algebraic equations by utilizing the fractional Taylor operational matrix of fractional integration. This system of equations can be solved efficiently. Some numerical examples are given to demonstrate the accuracy and applicability. The results show that the presented method is efficient and applicable.

scholarly journals Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 226-230 ◽  
Author(s):  
A. Bolandtalat ◽  
E. Babolian ◽  
H. Jafari
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Fractional Differential Equations ◽  
Numerical Solutions ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Algebraic Equations ◽  
Boubaker Polynomials ◽  
Fractional Differential ◽  
The Given

AbstractIn this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.

Highly accurate technique for studying some chaotic models described by ABC-fractional differential equations of variable-order

2020 ◽  
pp. 2150018
Author(s):  
M. M. Khader ◽  
Ibrahim Al-Dayel
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Polynomial Interpolation ◽  
Numerical Technique ◽  
Variable Order ◽  
Lagrange Polynomial ◽  
Efficient Tool ◽  
Fractional Differential ◽  
The Given

The propose of this paper is to introduce and investigate a highly accurate technique for solving the fractional Logistic and Ricatti differential equations of variable-order. We consider these models with the most common nonsingular Atangana–Baleanu–Caputo (ABC) fractional derivative which depends on the Mittag–Leffler kernel. The proposed numerical technique is based upon the fundamental theorem of the fractional calculus as well as the Lagrange polynomial interpolation. We satisfy the efficiency and the accuracy of the given procedure; and study the effect of the variation of the fractional-order [Formula: see text] on the behavior of the solutions due to the presence of ABC-operator by evaluating the solution with different values of [Formula: see text]. The results show that the given procedure is an easy and efficient tool to investigate the solution for such models. We compare the numerical solutions with the exact solution, thereby showing excellent agreement which we have found by applying the ABC-derivatives. We observe the chaotic solutions with some fractional-variable-order functions.

scholarly journals Topological optimization of the fork-end of a knuckle joint

2018 ◽  
Vol 27 (3-4) ◽  
Author(s):  
Naman Jain
Keyword(s):  
Finite Element ◽  
Parametric Design ◽  
Fuel Efficiency ◽  
Optimization Technique ◽  
Optimality Criteria ◽  
Topological Optimization ◽  
Optimality Criteria Method ◽  
Structural Compliance ◽  
The Given ◽  
Multiple Load

AbstractTopology optimization is a mathematical approach that optimizes the layout for the given design constraints such as loading and boundary conditions so that the optimum design obtained performs its function. In different types of loading conditions such as single load or multiple load topological optimization result in the best use of a material for a body in given volume constraints. In topological optimization the structural compliance is minimized while satisfying a constraint on the volume of the structure. This paper represents the topological optimization of the fork-end (double eye) of a knuckle joint with the objective to reduce the mass of an existing fork-end of a knuckle joint of an automobile or locomotive by applying the optimization technique. Reducing the weight of an automobile part will result in the overall weight reduction of a vehicle, thus, its energy consumption demands decrease thereby improving its fuel efficiency. The topological optimization was done using a finite element solver, ANSYS. The ANSYS Parametric Design Language was employed for utilizing the topological optimization capabilities of the commonly used finite element solver ANSYS. Solid92 elements were used to model and mesh the fork end of the knuckle joint in ANSYS. The optimality criteria method was used for topological optimizing the fork end of a knuckle joint.

scholarly journals Comparative Analysis of Genetically-Modified Crops: Conditional Equivalence Criteria

2021 ◽  
Author(s):  
Changjian Jiang ◽  
Chen Meng ◽  
Adam W. Schapaugh ◽  
Huizhe Jin
Keyword(s):  
Genetically Modified ◽  
Genetically Modified Crops ◽  
Genotypic Differences ◽  
Unintended Effects ◽  
Equivalence Test ◽  
History Of ◽  
Equivalence Criterion ◽  
The Difference ◽  
New Criterion ◽  
The Given

AbstractThe comparative assessment of genetically-modified (GM) crops relies on the principle of substantial equivalence, which states that such products should be compared to conventional counterparts that have an established history of safe use. In an effort to operationalize this principle, the GMO Panel of the European Food Safety Authority proposed an equivalence test that directly compares a GM test variety with a set of unrelated, conventionally-bred reference varieties with part of the difference as the known background of the test (the same as the given control). The criterion of the EFSA test, however, is defined solely by genotypic differences between the non-traited control and reference varieties (i.e. the background effect) while assuming the so-called GM trait effect as zero. As the outcome of an EFSA equivalence test is determined primarily by the similarity, or lack thereof, of the control and references, a conditional equivalence criterion is proposed in this investigation that focuses on “unintended” effects of a GM trait which is irrespective of the (random) genotypic value of a given control. The new criterion also includes a mean-scaled standard similar to the 80-125% rule for bioequivalence assessment practiced in the pharmaceutical industry as an alternative when the reference variation is zero or close to zero. In addition, optional criteria are proposed with a step-wise procedure to control the rate of false negatives (non-equivalence by chance) providing a comprehensive assessment under multiple comparisons. An application to maize grain composition data demonstrates that the conditional equivalence criterion provides effect-specific and more robust assessment of equivalence than the EFSA criterion did, especially for GM traits showing negligible or no unintended effects which are likely true for most traits in the current market.

scholarly journals Hybrid conjugate gradient parameter for solving symmetric systems of nonlinear equations

2019 ◽  
Vol 16 (1) ◽  
pp. 539
Author(s):  
M. K. Dauda ◽  
Mustafa Mamat ◽  
Mohamad A. Mohamed ◽  
Nor Shamsidah Amir Hamzah
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient ◽  
Numerical Solutions ◽  
Graphical Representation ◽  
Systems Of Nonlinear Equations ◽  
Inexact Line Search ◽  
Derivative Free ◽  
Gradient Parameter ◽  
The Given ◽  
Symmetric Systems

Mathematical models from recent research are mostly nonlinear equations in nature. Numerical solutions to such systems are widely needed and applied in those areas of  mathematics. Although, in recent years, this field received serious attentions and new approach were discovered, but yet the efficiency of the previous versions suffers setback. This article gives a new hybrid conjugate gradient parameter, the method is derivative-free and analyzed with an effective inexact line search in a given conditions. Theoretical proofs show that the proposed method retains the sufficient descent and global convergence properties of the original CG methods. The proposed method is tested on a set of test functions, then compared to the two previous classical CG-parameter that resulted the given method, and its performance is given based on number of iterations and CPU time. The numerical results show that the new proposed method is efficient and effective amongst all the methods tested. The graphical representation of the result justify our findings. The computational result indicates that the new hybrid conjugate gradient parameter is suitable and capable for solving symmetric systems of nonlinear equations.

A 3-R(SRS)RP Multi-Loop Mechanism for Space Manipulation: Design, Kinematics, Singularity, and Workspace

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Chuanyang Li ◽  
Hongwei Guo ◽  
Dewei Tang ◽  
Huiyin Yan ◽  
Rongqiang Liu ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
The Novel ◽  
Forward Displacement ◽  
Aerospace Applications ◽  
Wide Range ◽  
Variable Section ◽  
Varying Λ ◽  
Mapping Diagram ◽  
The Given ◽  
Novel Design

Abstract Space manipulation has great prospects in aerospace applications. In this work, a multiloop robot, namely 3-R(SRS)RP multiloop mechanism, is presented. Its design, kinematics, singularity, and workspace are studied. The novel design is mainly reflected in the robot’s structure, variable section, and novel compound hinge. Given these features, the forward-displacement undertaken with a closed-loop method leads to a complex mapping diagram. Only numerical solutions are obtained in this model due to the variable section parameter λ. This variable affects kinematic performances such as bending and folding properties. Moreover, the node differential kinematics and the Jacobian matrix are solved to analyze singular configurations of the mechanism. The workspace is then evaluated via a numerical method with varying λ. The bending and folding properties and the continuous workspace of the given robot vary while changing λ. Hence, the robot has great potentials of good performances in various applications. With this robot, a multimodule manipulator with a wide range of operations, increased mobility and rigidity, variable geometry, and adaptable shape based on mission requirements can be constructed.

Matrix Algorithm for Reliability of Structure in Generalized Random Space

2012 ◽  
Vol 166-169 ◽  
pp. 1913-1916
Author(s):  
Xiao Jie Liu ◽  
Xiao Jing Li ◽  
Wei Hua Shi ◽  
Ya Chuan Kuang
Keyword(s):  
Reliability Index ◽  
Limit State ◽  
Random Variable ◽  
State Equation ◽  
Matrix Algorithm ◽  
Covariance Propagation ◽  
The Given

In this paper variance of preformance function is calculated according to law of covariance propagation and matrix algorithm is used to calculate reliability index of structures in generalized random space, which is applicable to independent and correlative random variable, linear or nonlinear limit state equation. The given example has shown that the proposed method is very simple and convenient.

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