发布时间 : 星期二 文章2013美赛论文更新完毕开始阅读
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Taking the degree of uniformity of the distribution of the the bakeware edge heat (H) into account ,an objective function can be obtained:
Max CU?3.21?10?2r2?0.66?10?2r?90.76
Adding the weight analysis, we can obtain the total target function:
22??22?2Max ps??1?p?CU?p??4??r??r????1?p??3.21?10r?0.66?10r?90.76? 4????mn?WL1? Set : F?ps??1??pC U??Then we have Max F?p??4?r2??r2????1?p??3.21?10?2r2?0.66?10?2r?90.76?
4????mn?WL1?Also adding constraints :
WmW?1 and r?(0,)2nnLWL?4r2??r2?A mn
3.4 Model solving analyze :
Optimization model is obtained a fit r by gradually optimizing , use the change of rto describe the oven to maximize the number of baking pan and optimal heat evenly distributed degree .
In the planning model , with the change of the value of p ,maximum of the number of bracket bakeware and optimal heat uniform distribution of the degree are of mutual restraint ,Different value of pmake the model in the design pays different attention to the two constraints.Value of thepincreases, the models in the optimization process more biased in the oven space stent utilization problems and weaken the design considerations on the uniform distribution of heat . Value of the
pdecreases, the situation is different . Oven width to length ratio W/Laffects the
arrangement on the baking sheet in the oven bracket its optimized baking pan shape influence is weak.
3.5 Model deepening:
In model 2 ,through the establishment of a model we designed top plan which can both meet the the baking volume requirements ( oven rack space usage ) , but also
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give full consideration to the baking pan to heat evenly .Our model starts from the rack space utilization rate of 100% in design,each baking sheet in the holder was densely arranged baking pan , but in reality the pan is a three-dimensional kind , its every surface needs to get the heat from the oven space in the process of heating.Therefore, we need to consider sufficient gap is in contact with the oven space given the adjacent placing to the baking pan , so as to guarantee a constant thermal environment in the process of heating food .Expand Bakeware model to the three-dimensional space , consider the three-dimensional shape of the baking pan , and still meet the baking volume and uniformity of optimization .
The bakeware model expanding from the plane to the space , we increase the baking pan problem with the bottom surface of the side and the bottom surface in the edge angle optimization problem . In model 2 a more perfect bakeware plane model has been optimized for perspective bakeware different planes in parallel to xoy in the design are used this optimization bakeware plane . We need to consider the optimization of the bakeware the sides and the bottom of obliquity and the gap between adjacent bakeware in the design of the perspective bakeware , that is:
? The bakeware side tilt problem : In order to make a hotplate having a good
uniformity of the heat distribution , optimization at the corner are taken
tangentially connected.Therefore ?????2 .When the height of the oven is a
certain value, the smaller the inclined angle is , the larger the volume of the oven is, and the greater the effective utilization of space is.However , increasing ? the degree of uniformity of the distribution of heat the baking pan would be affected , so we need to weigh the gravity of ?, and select the most optimal value
? Corner radius r:In the hotplate height certain circumstances , based on the
conclusions of model 2 , the larger bakeware,the internal heat distribution more uniform.
? The three-dimensional spherical corner problem : Multiple surfaces intersect at
the corner , the clustering ability of the heat is very strong , so the processing of the three - dimensional spherical corner is very important , the better spherical the corners rounded , the hotplate heat distribution more uniform .
Figure 7 Oven bracket baking tray placed ( side view) schematic diagram
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Deepen and expand the model to find the optimal tilt angle ?, corner radius r, as well as a more comprehensive three-dimensional spherical corner .
Solving the optimal inclination angle ?,and the problem of the corner radius r, the model is basically the same with the above model , the main difference is that the transition from the plane to the perspective is still calculated the degree of uniform distribution of the heat from the area of transition to the volume , thus establishing the mathematical programming model.
4. Model application and promotion:
The brownies are not only for the taste buds of people to be provided with endless enjoyment , but also as a means of collective life for many housewives preparing for the family relaxed and happy . Simple production process , coupled with the ideal smart baking tools , it will be able to produce delicious brownies for family gatherings , friends talking , regulating mood as transfer goods . Brownie cake pan model we designed , because of its good utilization of space and giving full consideration to the uniformity of the heat , can be not only used to store a large number of production , but also for home-made . So the the brownies baking pan has a very practical application value .
5. Model advantages and disadvantages :
5.1 Advantages:
Our model start from the simplified model in the process of establishing , carrying the full analysis of the design of the two-dimensional case bakeware , then according to actual life expand baking sheet model to the three-dimensional space , and then carry out the analysis of optimization and parameters analysis .Though starting from the ideal situation , yet it can return to real life situations , make the model design and study more meaningful .
5.2 Disadvantages:
Some part of the model during the design process are set in a high ideal level, and have the design and optimization of the model built on the ideal level , however,many assumptions is not absolutely exist in reality , even minimal presence . For example, when establishing a first model we ignore the thermal radiation of the temperature distribution of the bakeware edge , however, the heat radiation is also an important
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source of the heat distribute on the hotplate edge . There is limited computing capacity and the lack of data training within us, leading to our model is not substantial quantifiable results partially, so it is not strongly persuasive. .
6. References
[1]
http://www.0532ts.com/html/recipe/09211014212315071.html [2]
Cheng Jianchun.Equations of mathematical physics and its approximate methods.[P],Beijing:Science Press,2006 [3]
Wei wei. Applied Math Toolbox Technical Manual.[P],National Defence Industry Press,2004 [4]
Han wenting,Wu pute,Yang Qing,etal.Advances and comparisons of uniformity evaluation index of sprinkle irrigation. [5]
Li Wei-gang, Zhu Xian-fu.Application of PDE tool box in magnetostatic field. Department of Electric Engineering, Tongji University, Shanghai 200331,China