Distributional analysis of boundary value problems in half-spaces - exemplified by Melan's problem of elastostatics

Kirchner G.

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Distributional analysis of boundary value problems in half-spaces - exemplified by Melan's problem of elastostatics

机译：半空间边值问题的分布分析-以梅兰的弹性静力学问题为例

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Using a result on the C-infinity-dependence (with respect to a distinguished variable) of solutions to partially hypoelliptic operators, we present a definition for Green's function which allows to prove a representation theorem. Afterwards we discuss the construction of a Green's matrix for Melan's problem of elastostatics using the reflection principle and single layer potentials. This involves the solution of convolution equations as well as the explicit computation of convolutions. In this special case also the question of uniqueness is investigated. (C) 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. [References: 11]

机译：利用部分次椭圆算子解的C-无穷依赖性（相对于变量）的结果，我们给出了格林函数的定义，该定义可以证明一个表示定理。随后，我们讨论了使用反射原理和单层电势构造梅兰弹性静力学问题的格林矩阵。这涉及到卷积方程的求解以及卷积的显式计算。在这种特殊情况下，还研究了唯一性问题。（C）2003 WILEY-VCH Verlag GmbH＆Co.KGaA，Weinheim。 [参考：11]

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《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2003年第9期|共6页
作者
Kirchner G.;
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正文语种 eng
中图分类应用数学;
关键词
Fundamental matrix; Green's tensor; Isotropic and homogeneous elastostatics in a half-plane; Melan's problem; Distributional solution;

机译：基本矩阵;Green张量;半平面上的各向同性和均质弹性体;Melan问题;分布解;

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1. Distributional analysis of boundary value problems in half-spaces - exemplified by Melan's problem of elastostatics [J] . Kirchner G. Zeitschrift fur Angewandte Mathematik und Mechanik . 2003,第9期

机译：半空间边值问题的分布分析-以梅兰的弹性静力学问题为例
2. A systematic derivation of Green's and Poisson's matrices for boundary-value problems in elastostatic half-spaces [J] . Gerhard Kirchner IMA Journal of Applied Mathematics . 2007,第3期

机译：弹性半空间中边值问题的格林和泊松矩阵的系统推导
3. Identification of Boundary Condition for Elastostatic Thin Plate Bending Problems (1st Report, BEM Analysis of Inverse Problems for Boundary Values) [J] . Masahiro ARAI, Satoshi OSHIMA, Tadaharu ADACHI 日本機械学会論文集. A編 . 1999,第632期

机译：确定弹性静力薄板弯曲问题的边界条件（第一个报告，边界值反问题的BEM分析）
4. Dynamic analysis of foundations in a half-space using a consistent transmitting boundary with continued-fraction absorbing boundary conditions [C] . Jin Ho Lee, Jae Kwan Kim, John L. Tassoulas International Conference on Structural Dynamics . 2011

机译：使用一致的传输边界与持续的分数吸收边界条件的半空间基础的动态分析
5. Coupled magneto-elastostatic analysis using implicit boundary finite element method. [D] . Zhang, Sung-Uk. 2010

机译：使用隐式边界有限元方法的磁弹耦合分析。
6. Roles of Boundary Conditions in DNA Simulations: Analysis of Ion Distributions with the Finite-Difference Poisson-Boltzmann Method [O] . Xiang Ye, Qin Cai, Wei Yang, 2009

机译：边界条件在DNA模拟中的作用：用有限差分泊松-玻尔兹曼方法分析离子分布
7. Distributional boundary values of harmonic potentials in Euclidean half-space as fundamental solutions of convolution operators in Clifford analysis [O] . Brackx Fred, De Bie Hendrik, De Schepper Hennie 2013

机译：欧几里得半空间中谐波势的分布边界值作为Clifford分析中的基本解或卷积算子
8. New Boundary Integral Equation Formulation for Elastodynamic and Elastostatic Crack Analysis [R] . Zhang, C., Achenbach, J. D. 1988

机译：弹性动力学和弹性静力裂纹分析的新边界积分方程公式

Distributional analysis of boundary value problems in half-spaces - exemplified by Melan's problem of elastostatics

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