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Titlebook: Mathematical Methods in Continuum Mechanics of Solids; Martin Kru?ík,Tomá? Roubí?ek Textbook 2019 Springer Nature Switzerland AG 2019 Cont

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發(fā)表于 2025-3-21 16:30:07 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Mathematical Methods in Continuum Mechanics of Solids
編輯Martin Kru?ík,Tomá? Roubí?ek
視頻videohttp://file.papertrans.cn/627/626253/626253.mp4
概述Serves as an advanced textbook for graduate students, as well as a monograph for theoretically oriented researchers.Merges rational continuum mechanics with mathematical analysis. Focuses on rigorous
叢書名稱Interaction of Mechanics and Mathematics
圖書封面Titlebook: Mathematical Methods in Continuum Mechanics of Solids;  Martin Kru?ík,Tomá? Roubí?ek Textbook 2019 Springer Nature Switzerland AG 2019 Cont
描述.This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited..This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields..?.
出版日期Textbook 2019
關(guān)鍵詞Continuum Mechanics of Solids; Mathematical Methods in Continuum Mechanics of Solids; Thermodynamics; C
版次1
doihttps://doi.org/10.1007/978-3-030-02065-1
isbn_softcover978-3-030-02064-4
isbn_ebook978-3-030-02065-1Series ISSN 1860-6245 Series E-ISSN 1860-6253
issn_series 1860-6245
copyrightSpringer Nature Switzerland AG 2019
The information of publication is updating

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發(fā)表于 2025-3-21 21:59:00 | 只看該作者
Linear Rheological Models at Small Strainsdox is counted in a so-called . (sometimes denoted by the Hebrew letter ‘daleth’, .) defined as a ratio between the relaxation time and the observation time. The difference between solids and fluids is thus reflected by this number: large . means that the medium can be well understood as . while small . indicates rather a ..
板凳
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地板
發(fā)表于 2025-3-22 06:14:56 | 只看該作者
Description of Deformable Stressed Bodiesg for the external ones is introduced axiomatically and its existence is fundamental for continuum mechanics of solids. In order to map stress fields from the deformed to the reference configurations, we introduce the so-called Piola transform which formally allows for the same form of equilibrium equations in both configurations.
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發(fā)表于 2025-3-22 11:45:22 | 只看該作者
Elastic Materialselations should involve the stress tensor and the deformation gradient and may be in general implicit, cf. (Rajagopal, Appl Math, 48:279–319 (2003), [409]). Without excluding too many applications, we confine ourselves to the case when the stress is explicitly determined by the strain.
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發(fā)表于 2025-3-22 16:53:20 | 只看該作者
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發(fā)表于 2025-3-22 19:33:53 | 只看該作者
Linearized Elasticityitates computational algorithms substantially, and there is no wonder that most engineering computations in solid mechanics are just based on such hypotheses. As we will see, linearized elasticity provides us with unique solutions and strongly relies on convexity assumptions.
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