Abstract
How to make a sandcastle with good stability is an interesting modeling problem, the core of which is how to design the shape of its foundation and select appropriate material so that it can fully resist wave erosion. First, we design the Foundation Shape Optimization (FSO) Model to obtain the geometric shape that last longest. By pre-screening, we preliminarily select the circular truncated cone. Then we analyse the impact force of the sea waves, list the constraint conditions and calculate the optimal parameters for it. Second, the water-to-sand mixture is identified by microcosmic Normalized Extremum Model. Before getting results, the Ideal Sand Particles Plane (ISPP) Model helps us figure out the equivalent relationship among three functions. Finally, we get the objective function through normalization and work out the best proportion (13.14%) with the optimal sub-humid angle through Genetic Algorithm (GA).
Highlights
Each year, various sandcastle contests are held all over the world, especially in America
The sea wave is a wave of the ocean water produced by the wind
To specify and visualize the forces on the sandcastles, we only consider the main impact of the sea waves on the sandcastle foundation
Summary
Various sandcastle contests are held all over the world, especially in America. Successive waves continuously wash over the elaborately built sandcastles. When the wave reaches the coast or the shallow water, its depth becomes shallow, length becomes short, height becomes large, and direction is refracted, due to the influence of terrain. We normally see waves slowly washing over sandcastles by the seashore, which can be seen as the horizontal force. In addition to the gravity itself, raindrop splashing and shoreline erosion could wash away or even soak the sand nearby, which would cause the sandcastles to collapse. The water-to-sand proportion has a decisive influence on the stability of the foundation [2]. We take multiple factors into consideration, including the foundation shape and the water-to-sand mixture proportion. Considering its function and the effect of waves, we choose a truncated cone for the foundation instead of a prismoid. The shape of the truncated cone is discussed in detail, and its optimal values of the parameters are obtained
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