A Reconciliation of Local and Global Models for Bone Remodeling Through Optimization Theory

1999 ◽  
Vol 122 (1) ◽  
pp. 72-76 ◽  
Author(s):  
G. Subbarayan ◽  
D. L. Bartel
Keyword(s):  
Optimization Theory ◽  
Optimality Criteria ◽  
Bone Architecture ◽  
Necessary Condition ◽  
Local Error ◽  
Mathematical Form ◽  
Global Models ◽  
Load Bearing ◽  
Global Criterion ◽  
The Cost

Remodeling rules with either a global or a local mathematical form have been proposed for load-bearing bones in the literature. In the local models, the bone architecture (shape, density) is related to the strains/energies sensed at any point in the bone, while in the global models, a criterion believed to be applicable to the whole bone is used. In the present paper, a local remodeling rule with a strain “error” form is derived as the necessary condition for the optimum of a global remodeling criterion, suggesting that many of the local error-driven remodeling rules may have corresponding global optimization-based criteria. The global criterion proposed in the present study is a trade-off between the cost of metabolic growth and use, mathematically represented by the mass, and the cost of failure, mathematically represented by the total strain energy. The proposed global criterion is shown to be related to the optimality criteria methods of structural optimization by the equivalence of the model solution and the fully stressed solution for statically determinate structures. In related work, the global criterion is applied to simulate the strength recovery in bones with screw holes left behind after removal of fracture fixation plates. The results predicted by the model are shown to be in good agreement with experimental results, leading to the conclusion that load-bearing bones are structures with optimal shape and property for their function. [S0148-0731(00)00601-4]

Economic feasibility of restoration of degraded and neglected lands

2020 ◽  
pp. 79-90
Author(s):  
Anastasiya V. Mironova ◽  
Igor’ V. Liskin ◽  
Irina I. Afonina
Keyword(s):  
Soil Layer ◽  
Black Soil ◽  
Economic Feasibility ◽  
Research Purpose ◽  
Necessary Condition ◽  
Labor Costs ◽  
Human Needs ◽  
Fallow Lands ◽  
The Cost ◽  
Regions Of Russia

Neglect of soils leads to their degradation, worsens useful properties, and reduces fertility and productivity. (Research purpose) The research purpose is in conducting a comparative analysis of technologies for treating degraded soils, taking into account the economic feasibility of their restoration in non-black-soil regions of Russia. (Materials and methods) The article shows the main technological scheme of restoration of degraded soils. Authors have identified the main groups of land that are located in non-black-soil regions of Russia. (Results and discussion) The article presents the need for equipment, economic and labor costs for the restoration of each type of land in the non-black-soil regions of Russia. Authors took into account that the salary of machine operators depends on the time of direct execution of the task. It was found that the restoration of virgin and fallow lands was the most preferable from the economic, energy-saving and environmental points of view. The article shows that the restoration of pasture areas exceeds the cost of processing virgin lands, but the number of necessary machine and tractor units is comparable to work on virgin lands. Authors recommend to develop the soils with woody and shrubby vegetation in the first place, starting with land occupied by young plants. It is necessary to take into account the criteria for the fertility of the soil layer. It was found that soils with a small excess of moisture have small cost of its development, while on heavily swampy soils the cost of work on their development is many times higher than the cost of restoring other types of land. (Conclusion) The article shows that the restoration of neglected land is a necessary condition for improving the provision of human needs for food and a number of industrial goods. First of all, it is necessary to develop land that requires minimal investment of economic and labor costs.

Finding the optimum layout for cable-stayed bridge in conceptual design

2021 ◽  
Author(s):  
Sami Soppela ◽  
Esko Järvenpää
Keyword(s):  
Longitudinal Direction ◽  
Simple Calculation ◽  
Integral Calculus ◽  
Bearing Material ◽  
Load Bearing ◽  
Permanent Load ◽  
Early Design Stages ◽  
Cable Forces ◽  
The Cost ◽  
Cable Stayed Bridges

<p>In the cable-stayed bridges the primary cost components of the load-bearing material, in the longitudinal direction of the bridge, are the cables. The longer the bridge, the higher the share of the costs of the load-bearing material. The quantity of the cables and the cost optimized cable and tower topology can be reliably solved, already in very early design stages, using a simple calculation method proposed in this article. The cables are considered as a curtain structure and the cable forces are calculated for the permanent load balance. The solutions are performed mathematically by using integral calculus based on a force length method and a unit bridge concept. The results provide a good idea of the optimum pylon height for both one-pylon and two-pylon bridges. The optimum pylon height depends on the span ratio and the chosen cable system.</p>

scholarly journals Mechanics of evolutionary digit reduction in fossil horses (Equidae)

2017 ◽  
Vol 284 (1861) ◽  
pp. 20171174 ◽  
Author(s):  
Brianna K. McHorse ◽  
Andrew A. Biewener ◽  
Stephanie E. Pierce
Keyword(s):  
Body Mass ◽  
Bone Geometry ◽  
Continuous Measure ◽  
Positive Allometry ◽  
Load Bearing ◽  
Beam Analysis ◽  
Body Sizes ◽  
Major Trend ◽  
The Cost

Digit reduction is a major trend that characterizes horse evolution, but its causes and consequences have rarely been quantitatively tested. Using beam analysis on fossilized centre metapodials, we tested how locomotor bone stresses changed with digit reduction and increasing body size across the horse lineage. Internal bone geometry was captured from 13 fossil horse genera that covered the breadth of the equid phylogeny and the spectrum of digit reduction and body sizes, from Hyracotherium to Equus . To account for the load-bearing role of side digits, a novel, continuous measure of digit reduction was also established—toe reduction index (TRI). Our results show that without accounting for side digits, three-toed horses as late as Parahippus would have experienced physiologically untenable bone stresses. Conversely, when side digits are modelled as load-bearing, species at the base of the horse radiation through Equus probably maintained a similar safety factor to fracture stress. We conclude that the centre metapodial compensated for evolutionary digit reduction and body mass increases by becoming more resistant to bending through substantial positive allometry in internal geometry. These results lend support to two historical hypotheses: that increasing body mass selected for a single, robust metapodial rather than several smaller ones; and that, as horse limbs became elongated, the cost of inertia from the side toes outweighed their utility for stabilization or load-bearing.

ONE OF THE POSSIBLE APPROACHES FOR DESIGNING A HOB CUTTER FOR MACHINING A SMALL CYCLOIDAL CONE

2021 ◽  
pp. 97-103
Author(s):  
В.В. Куц ◽  
А.А. Панин ◽  
Д.Н. Тютюнов ◽  
К.В. Жилина
Keyword(s):  
Gear Wheel ◽  
Front Surface ◽  
Necessary Condition ◽  
Machining Accuracy ◽  
Small Range ◽  
New Approach ◽  
Main Requirement ◽  
Number Of Factors ◽  
Gear Wheels ◽  
The Cost

Предлагается краткий обзор промышленного производства червячных фрез. Показано, что повышение качества и производительности изготовления зубчатых колес является необходимым условием снижения себестоимости и расширения объемов производства зубчатых колес на отечественных предприятиях. Главным требованием, предъявляемым к зубьям данной фрезы, является то, чтобы в результате заточки по передней поверхности, которая лежит в осевой плоскости фрезы, профиль зубьев сохранялся до почти полного их износа. Поэтому особое внимание уделяется выбору кривой затылования с учётом целого ряда факторов, способствующих совершенствованию процесса обработки. Отмечено, что затылование имеет ряд преимуществ, в сравнении с острой заточкой фрез. Изложен новый подход к проектированию рабочей оснастки для обработки малых колес циклоидной передачи и исследованы теоретически допустимые интервалы изменения задних углов при затыловании. Установлено, что несмотря на преимущества циклоидальной фрезы перед другими типами затылованных фрез в скорости и точности обработки, она имеет один недостаток - довольно малый промежуток применимости на дуге циклоиды. На основе существующих подходов разработан вариант затылования зубьев червячной фрезы по циклоиде The article provides an overview of the industrial production of hob cutters. We show that improving the quality and productivity of gear wheel manufacturing is a necessary condition for reducing the cost and expanding the production of gear wheels at domestic enterprises. The main requirement for the teeth of this cutter is that, as a result of sharpening on the front surface, which lies in the axial plane of the cutter, the profile of the teeth remains sharp until they are almost completely worn out. Therefore, we paid special attention to the choice of the relief curve, taking into account a number of factors that contribute to the improvement of the processing process. We note that relief has a number of advantages in comparison with sharpening of cutters. We give a new approach to the design of working equipment for processing small cycloidal wheels and investigate the theoretically permissible intervals of variation of the rear angles during relief. We established that despite the advantages of a cycloidal cutter over other types of undercut cutters in terms of speed and machining accuracy, it has one drawback - a rather small range of applicability on the cycloid arc. On the basis of existing approaches, we developed a variant of the relief of the teeth of the worm cutter along the cycloid

New Standard for Assessment of Structural Integrity for Existing Load-Bearing Structures-Norsok N-006

2009 ◽  
Author(s):  
Gunnar Solland ◽  
Inge Lotsberg ◽  
Lars G. Bjo̸rheim ◽  
Gerhard Ersdal ◽  
Vidar-Andre´ Gjerstad ◽  
...  
Keyword(s):  
Structural Integrity ◽  
Regulatory System ◽  
Life Extension ◽  
Design Standards ◽  
Load Bearing ◽  
Fatigue Design ◽  
Design Life ◽  
Advanced Analysis ◽  
The Cost ◽  
Existing Structure

An increasing number of platforms in the Norwegian continental shelf are reaching their design life. For various reasons these platforms will require an assessment of their structural integrity. When performing these assessments the engineer is faced with tasks where little guidance is found in design standards, for several reasons. The two most important being: 1) The analyses that is performed in a typical assessment of existing structure is often applying very advanced techniques and methodology that seldom is used in design of new structures, as the cost of doing advanced analysis is relatively low compared to replacement of an existing structure, but relatively high compared to moderate additions of e.g. steel in the design of a new structure. 2) Design standards are based on theories, methods and experience for structures in a given design life (e.g. fatigue design and corrosion protection design). When this design life is extended, sound methods for ensuring that the structures are still sufficient safe is needed. Such methods will normally be “condition based design”, where inspection, maintenance and repairs are included in the assessment in integrated way. Such methods are not given in normal design standards. For these reasons a new NORSOK standard is developed that gives recommendation on how to deal with the specific aspects that engineers meet when performing assessments of structures in general, but also specifically for assessment for life extension. The standard is named “Standard for Assessment of Structural Integrity for Existing Load-bearing Structures” and is issued as a NORSOK standard and given the number N-006 [1]. The topics that are covered in the standard include: Shut down and unmanning criteria for platforms not meeting ordinary requirements, specific issues for determination of ultimate capacities by use of non-linear methods, cyclic capacity checks, fatigue life extension, requirements to in-service inspection etc. The paper describes the background and the content of the new standard and it presents examples of recommendations given. The role of the new standard in the Norwegian regulatory system is shown.

scholarly journals Efficient designs for sampling and subsampling in fisheries research based on ranked sets

2009 ◽  
Vol 66 (5) ◽  
pp. 928-934 ◽  
Author(s):  
You-Gan Wang ◽  
Yimin Ye ◽  
David A. Milton
Keyword(s):  
Simple Random Sampling ◽  
Optimality Criteria ◽  
Abundance Index ◽  
Sampling Schemes ◽  
Concomitant Variables ◽  
Monitoring Survey ◽  
Catch Rates ◽  
The Cost ◽  
Selection Of ◽  
Age Prediction

Abstract Wang, Y-G., Ye, Y., and Milton, D. A. 2009. Efficient designs for sampling and subsampling in fisheries research based on ranked sets. – ICES Journal of Marine Science, 66: 928–934. Sampling strategies are developed based on the idea of ranked set sampling (RSS) to increase efficiency and therefore to reduce the cost of sampling in fishery research. The RSS incorporates information on concomitant variables that are correlated with the variable of interest in the selection of samples. For example, estimating a monitoring survey abundance index would be more efficient if the sampling sites were selected based on the information from previous surveys or catch rates of the fishery. We use two practical fishery examples to demonstrate the approach: site selection for a fishery-independent monitoring survey in the Australian northern prawn fishery (NPF) and fish age prediction by simple linear regression modelling a short-lived tropical clupeoid. The relative efficiencies of the new designs were derived analytically and compared with the traditional simple random sampling (SRS). Optimal sampling schemes were measured by different optimality criteria. For the NPF monitoring survey, the efficiency in terms of variance or mean squared errors of the estimated mean abundance index ranged from 114 to 199% compared with the SRS. In the case of a fish ageing study for Tenualosa ilisha in Bangladesh, the efficiency of age prediction from fish body weight reached 140%.

Load Bearing and Mass Relation Contrast between Composite Shell and Alloy Shell

2013 ◽  
Vol 703 ◽  
pp. 217-220
Author(s):  
Hai Peng Gao ◽  
Meng Liu ◽  
Jun Wang
Keyword(s):  
Load Condition ◽  
Optimization Theory ◽  
State Theory ◽  
Parametric Modeling ◽  
Mass Relation ◽  
Work Efficiency ◽  
Load Bearing ◽  
Influence Curves ◽  
Weight Condition ◽  
Distortion Energy

To improve work efficiency of cabin and solve the contradiction between load bearing and mass, combining parametric modeling and optimization theory,the influence curves of load bearing on mass are proposed. Applying stress state theory, combining distortion energy theory criterion and Tsai-Wu failure criterion, shells load bearing is theoretically analysed. Contrast results are, in the same load condition, compared with alloy, the weight of composite reduces 46.2%;in the same weight condition, the load bearing of composite increases 75%. At present, the cabin load bearing is 0.04MPa, to improve work efficiency, increasing to 0.055MPa and replacing alloy by composite, the load bearing increases 37.5%, while the weight reduces 26.1%, then the contradiction between work efficiency and mass is coordinated.

scholarly journals Numerical Modelling Of The Strengthening Process Of Steel-Concrete Composite Beams

2015 ◽  
Vol 19 (4) ◽  
pp. 99-110 ◽  
Author(s):  
Piotr Szewczyk ◽  
Maciej Szumigała
Keyword(s):  
Numerical Modelling ◽  
Bearing Capacity ◽  
Composite Beam ◽  
Steel Plate ◽  
Composite Beams ◽  
Steel Beam ◽  
Load Bearing Capacity ◽  
Load Bearing ◽  
Main Assumption ◽  
The Cost

Abstract This paper presents the numerical modelling of strengthening a steel-concrete composite beam. The main assumption is that the strengthening is not the effect of the state of a failure of a structure, but it resulted from the need to increase the load-bearing capacity and stiffness of the structure (for example: due to a change in the use of the object). The expected solution is strengthening without the necessity to completely unload the structures (to reduce the scope of works, the cost of modernization and to shorten the time). The problem is presented on the example of a composite beam which was strengthened through welding a steel plate to the lower flange of the steel beam. The paper describes how energy parameters are used to evaluate the efficiency of structures’ strengthening and proposes an appropriate solution.

scholarly journals A Note on Optimal Control Problem Governed by Schrödinger Equation

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Yusuf Koçak ◽  
Ercan Çelik ◽  
Nigar Yıldırım Aksoy
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Schrödinger Equation ◽  
Optimal Control Problem ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Optimal Solution ◽  
Necessary Condition ◽  
Existence And Uniqueness Theorem ◽  
The Cost

AbstractIn this work, we present some results showing the controllability of the linear Schrödinger equation with complex potentials. Firstly we investigate the existence and uniqueness theorem for solution of the considered problem. Then we find the gradient of the cost functional with the help of Hamilton-Pontryagin functions. Finally we state a necessary condition in the form of variational inequality for the optimal solution using this gradient.

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