| 引用本文: | 冯晓九,梁立孚.反映的规律为本构关系的变分原理[J].哈尔滨工业大学学报,2016,48(4):149.DOI:10.11918/j.issn.0367-6234.2016.04.025 |
| FENG Xiaojiu,LIANG Lifu.The variational principle：the law of reflection is constitutive relation[J].Journal of Harbin Institute of Technology,2016,48(4):149.DOI:10.11918/j.issn.0367-6234.2016.04.025 |
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| 摘要: |
| 为证明经典变分原理中存在反映的规律为本构关系的变分原理，从非线性弹性动力学的基本方程出发，应用变积方法建立非线性弹性动力学Hamilton原理.再应用对合变换法、Lagrange乘子法和局部代入法，将Hamilton原理变换为本构变分原理.论证了该变分原理反映的规律为本构关系，本研究以非线性材料为例，找到了一个新的材料本构关系的获得途径，为数值建模提供了理论依据.研究结果表明，补充和完善了经典变分原理中对3类基本规律的反映，即：最小势能原理反映的规律为平衡关系、最小余能原理反映的规律为连续关系和本构变分原理反映的规律为本构关系.
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| 关键词: 非线性弹性动力学 变积 本构关系 变分原理 对合变换 Lagrange乘子法 局部代入法 |
| DOI：10.11918/j.issn.0367-6234.2016.04.025 |
| 分类号:O343 |
| 文献标识码:A |
| 基金项目:国家自然科学基金 (10272034). |
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| The variational principle：the law of reflection is constitutive relation |
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FENG Xiaojiu1, LIANG Lifu2
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(1.School of Environmental and Safety Engineering, ChangzhouUniversity, 213164 Changzhou, China; 2.College of Aerospace and Civil Engineering, Harbin Engineering University, 150001 Harbin, China）
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| Abstract: |
| In order to prove that the classical variational principles contain one principle that the reflection law is the constitutive relation, Hamilton principle of nonlinear elastodynamics is established by using the variational integral, starting from the basic equations of nonlinear elastodynamics. Then, after involutory transformation is used, Hamilton theory is converted to the constitutive variational principle with Langrange multiplier method and partial substitution method. It testifies that this variational principle reflects the constitutive relation. Taking the nonlinear material as an example, a new way to obtain the material constitutive relation is provided in this paper, which provides theoretical basis for numeral modeling. It supplements and improves the reflections of three basic rules in the classical constitutive relation:the reflection law of minimum potential energy principle is the balanced relation, the reflection law of the minimum complimentary energy principle is continuous relation, and the reflection law of constitutive variational principle is constitutive relation.
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| Key words: nonlinear elastodynamics variational integral constitutive relation variational principle involutionary transformation Lagrange multiplier method partial substitution method |
