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Shell theory is a study of elastic mechanics, which studies the mechanical properties of thin shells under various loads, such as deformation, internal force distribution law, etc. Shells are also the object of study in structural mechanics. The so-called shell is an object surrounded by two curved surfaces, the inner and the outside, and the two curved surfaces are called the surface of the shell.
The surface formed by a point equidistant from the two surfaces is called the middle surface of the shell; The length of the midface normal between two surfaces is called the thickness of the shell. In general, the shell can be described by the geometry and thickness of the middle surface. A shell with a closed middle face is called a closed shell, otherwise it is called an open shell.
In addition to the inner and outer surfaces, the open shell has boundary surfaces on all sides. A shell with a maximum thickness much less than the radius of curvature of the middle surface and dimensions in the other two directions is called a thin shell. The thin shell mainly bears the external load with the mid-surface stress evenly distributed along the thickness rather than the bending stress that changes along the thickness, and has the advantages of light weight and high strength, so it is widely used in aerospace, aviation, shipbuilding, chemical industry, construction, water conservancy and machinery industries.
The thin shell theory was developed at the end of the 19th century on the basis of Kirchhoffleff's hypothesis. After entering the 20th century, under the impetus of production technology, the shell theory has been greatly developed. At that time, various simplification theories were mainly developed for different types of shells.
In the 50s, the Kirchhoff hypothesis was revised to make the thin shell theory precise. With the advancement of electronic computers, the thin shell theory has developed rapidly in both numerical calculations and the combination of theoretical analysis and numerical calculations. Basic Theory The geometry and deformation of thin shells are often complex, and a series of simplified assumptions must be introduced before they can be studied.
The most commonly used assumption is Kirchhoff's hypothesis, on the basis of which a system of differential equations for thin shells can be established, and displacements and stresses in the shell can be obtained by solving the system of differential equations. Kirchhoff Lev hypothesized H. 1874 in GermanyAaron generalized Kirchhoff's hypothesis from sheet theory to shells.
In 1888, it was revised by Lefu in England to form the thin shell theory that is still widely used today. Kirchhoff's hypothesis consists of four things: the thickness of the shell (t) is much smaller than the minimum radius of curvature r of the middle surface; The deformation and displacement of the shell are very small, and the rotation angle and strain are small quantities of the same order, and the higher-order terms above the second degree can be ignored in the deformation geometric relationship. The normal stress component in the normal direction of the middle surface is much smaller than the normal component in the perpendicular direction, and the former can be omitted in the stress-strain relationship. The normal of the middle surface before deformation remains normal after deformation, and the thickness of the shell does not change during deformation.
Strictly speaking, the two assumptions are incompatible, but the resulting error is on the order of t r, which is permissible for thin shells.
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The world, there is no wonder, in our impression, everything in the world basically can not escape Newton's three laws, but there is such a sentence in the world, there is no absolute everything, everything has exceptions, today I will introduce to you 3 magical things that violate the laws of physics, Newton did not know after seeing it.
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There are many things that are wonderful, and here are some examples: Friendly lead.
The universe: its infinite boundaries, its mysterious dark matter and dark energy, and the planet full of life, all make people feel infinitely curious and amazed.
Brain: The human brain is a complex organ with tens of billions of neurons and trillions of neuronal connections. The mystery of the brain lies in how it generates consciousness and thinking.
Mathematics: Mathematics is a wonderfully combative subject with endless possibilities and a beautiful structure. Mathematics has a wide range of applications, from physics to computer science.
Life: Life is an incredible phenomenon that encompasses all life forms from tiny single-celled organisms to complex multicellular organisms. People are amazed by the diversity and adaptability of life.
Art: Art is a way of expressing emotions and thoughts, and it can be expressed in various forms such as painting, **, literature, and drama. The wonderful thing about art is that it can trigger people's emotions and imagination, and make people feel the shock of their hearts.
Technology: Technology is a force that transforms and improves human life, and it can bring convenience and efficiency. The wonder of modern technology is its rapid development and continuous innovation, such as artificial intelligence, virtual reality, and blockchain, which are all changing the way people live.
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There are many things that are wonderful, and the following are some examples:
Nature: The beauty and diversity of nature is amazing and appreciated. From majestic mountains and vast oceans to tiny flowers and insects, nature is full of wonderful sights and life forms. Repentance.
Science: Science allows us to better understand the nature of the world and the universe. From microscopic atoms and molecules to macroscopic planets and galaxies, science reveals endless mysteries and possibilities.
Art: Art is an expression of creativity and imagination that touches our emotions and souls. Painting, literature, film and other forms of art all have different charms and expressions, allowing us to feel the wonder of different cultures and spirits.
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The human world is full of all kinds of wonderful things, some of which are listed below:
1.The planetary and satellite systems in the solar system are full of mysteries and unknowns.
2.Biodiversity, including fascinating plants, animals and microorganisms, showcases the wondrous beauty of nature.
3.Ancient civilizations, such as China's Silk Road, Egypt's pyramids, and the mysteries of the Mayan civilization, are important sources for us to understand human history and culture.
4.Human creativity, achievements in the fields of literature, art, and science, all demonstrate the wonder and infinite potential of human beings.
5.The unsolved mysteries of the universe and the black holes, dark matter and dark energy in the universe are also the wonders of human exploration of the unknown world. Demolition and dismantling.
These are just some of the many wonderful things that surround us with endless inspiration and imagination.
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With the rapid development of modern technology, our world is becoming more and more diverse and interesting. Whether in life or in the field of academic research, there are more and more novelties and discoveries. In this article, we'll ** some of the latest and most unique things.
Artificial intelligence has become a new hot field.
In recent years, AI technology has made amazing progress and has become a hot topic in the tech world. Today's AI systems are capable of analyzing and performing complex data and performing highly complex tasks such as self-driving cars, speech recognition, image recognition, and more. As industry insiders in this field, we can look forward to more opportunities in the future to use AI technology to solve the problems we face.
Wearables change the way we live.
Wearables are another technology product that has gained a lot of attention in recent years. These devices embed sensors and computer technology into our everyday items such as clothing, glasses, watches, etc., helping us monitor health in real time, track fitness progress, provide navigational information, and more. These devices are changing the way we live, making us healthier, more active, and smarter.
The rise of virtual reality.
Virtual reality technology is widely used in the entertainment and gaming fields, but it also has a wide range of applications. With virtual reality, we can simulate real-world scenarios in the lab for training doctors, soldiers, and other professionals. In addition, virtual reality technology can also be applied to areas such as cybersecurity, advertising, and market research.
The future of gene technology.
Gene technology is an emerging biotechnology that allows us to have complete control and alteration over the genome of an organism. This technology has great potential to solve many medical problems such as cancer, genetic defects, etc. However, due to the serious ethical and ethical issues that genetic technology means for human beings, the application of this technology still needs to be deeply studied and explored.
Conclusion The above areas are just the tip of the iceberg of today's novelties. True innovation and discovery are always coming out that challenge our vision and imagination. We look forward to seeing more novelties emerge in various fields such as technology, industry, medical care, transportation, and environmental protection.
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There is a heavenly blue sky: white envy staring at clouds, sunset, morning glow, flowing clouds, sun, moon, star socks and stars, meteors, sunset, rising sun, breeze, rainbow.
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I think fate is a wonderful thing.
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I feel that I have gone astray silently, which is my usual health regimen.
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Magical magic.
Magical puppy.
Magical Sekiya (just kidding).
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The boat of friendship. From the comic book writer Antoni's original comic "The Boat of Friendship": two cute penguins sit together in a small boat, and there is a dialogue of "not speculation" that eventually leads to "the boat of friendship overturns".
I had some magical experience of transforming clothes, for example, when I was in high school, I felt that the school uniform was very ill-fitting, so I went to the tailor to cut the clothes, but in the end it didn't satisfy me, so I think it was very impressive.
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