<>思路和理解

*
<>问题中心:沙堡生存期仿真建模

<>题目要求:

*
基础沙堡模型。
第一问不同三维形状的模型需要满足相同的基本条件①距离水的距离②沙子类型③水沙比例。

问题细节:需要定义水域与沙堡的距离(下称水堡距)、沙堡毁灭的标准、沙堡的形状类型、水浪冲刷的量化影响(同时考虑每次冲刷对上次冲刷的相互影响)、不同水沙组合可以获得的最大应力(需要有土建专业基础)等,构建沙堡状态与上述变量的非线性模型,每个变量是关于时间的函数。

*
优化模型

第二问相对较简单,简单问题要做的漂亮。控制水堡距、日照、风蚀等相关因素,分别对每种形状的沙堡寻优,求取最佳水沙比例的具体范围,注意上述变量有可能是水沙比例的函数。

*

考虑雨水影响的沙堡模型。构建雨水冲击力的影响模型,同样建立为时间的函数,加入到问题一的模型中即可,评价不同三维形状沙堡在考虑该因素前后的生命长度。(圆锥形或许在该情况下是最佳结构,而在问题一种并非最佳)

*
那就再考虑下其他想法呀!不同形状组合、给沙堡加个围墙、排水沟…建议没有沙滩经历的同学先开头脑风暴聊一聊。具体模型改进无非完善模型,使得沙堡生命周期更持久。

*

写一份1-2页的文章,深入浅出通俗易懂的向杂志读者表达你们的结论,什么样的沙堡给孩子建立更有成就感,不受到人为干预可以存在多少多少年…注意严谨又不失内涵的表达方式。

* 该问题的亮点在于模型的可视表达,如每个三维沙堡不同生命周期的演化,单独某因素(降雨)的影响演化。
<>原题目翻译

<>原文

2020 MCM Weekend 2
Problem B: The Longest Lasting Sandcastle(s)
Wherever there are recreational sandy ocean beaches in the world, there seem
to be children (and
adults) creating sandcastles on the seashore. Using tools, toys, and
imagination, beach goers
create sandcastles that range from simple mounds of sand to complicated
replicas of actual
castles with walls, towers, moats, and other features that mimic real
castles. In all these, one
typically forms an initial foundation consisting of a single, nondescript
mound of wetted sand,
and then proceeds to cut and shape this base into a recognizable
3-dimensional geometric shape
upon which to build the more castle-defining features.
Inevitably, the inflow of ocean waves coupled with rising tides erodes
sandcastles. It appears,
however, that not all sandcastles react the same way to waves and tides, even
if built roughly the
same size and at roughly the same distance from the water on the same beach.
Consequently, one
wonders if there exists a best 3-dimensional geometric shape to use for a
sandcastle foundation.
Requirements

* Construct a mathematical model to identify the best 3-dimensional geometric
shape to use as a
sandcastle foundation that will last the longest period of time on a seashore
that experiences
waves and tides under the following conditions:
 built at roughly the same distance from the water on the same beach, and
 built using the same type of sand, roughly the same amount of sand, and the
same waterto-sand proportion.
* Using your model, determine an optimal sand-to-water mixture proportion for
the castle
foundation, assuming you use no other additives or materials (e.g. plastic or
wooden supports,
stones, etc.).
* Adjust your model as needed to determine how the best 3-dimensional
sandcastle foundation
you identified in requirement 1 is affected by rain, and whether it remains
the best 3-dimensional
geometric shape to be used as a castle foundation when it is raining.
* What other strategies, if any, might you use to make your sandcastle last
longer?
* Finally, write an informative, one- to two-page article describing your
model and its results for
publication in the vacation magazine: Fun in the Sun, whose readers are
mainly non-technical.
Your submission should consist of:
 One-page Summary Sheet
 Table of Contents
 One- to Two-page Article
 Your solution of no more than 20 pages, for a maximum of 24 pages with your
summary,
table of contents, and article.
Note: Reference List and any appendices do not count toward the page limit
and should appear
after your completed solution. You should not make use of unauthorized images
and materials
whose use is restricted by copyright laws. Ensure you cite the sources for
your ideas and the
materials used in your report.

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