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1.
提出了一种基于弹性力学第一性原理的数据驱动力学建模方法,其能够从基于弹性力学方程的数值计算结果建立简洁且能准确捕捉变形机制的力学模型。基于有限元计算得到的高精度数据和无监督数据驱动控制方程识别方法Seq-SVF,从梁的载荷和位移数据中自动识别出了Timoshenko梁形式的弯曲控制微分方程,得到了三种不同加载条件下剪切影响系数关于结构尺寸和力学参数的函数表达式。揭示了经典模型适用的加载条件,同时还给出了一种未发现的新模型。通过将基于弹性力学的第一性原理计算与数据驱动范式相结合,克服了传统建模方法的局限性和对人类经验的强依赖性,为建立简洁的力学模型提供了一种新途径。  相似文献   

2.
工程力学矢量的规范表示与弹性力学的不变性   总被引:3,自引:0,他引:3  
通过引入规范变换,消除了工程力学矢量数学表示上的物理缺陷,使规范化力学矢量与力学张量具有物理上的等价表示,从而奠定了不变性弹性力学的基础,为它在不同坐标下的具体应用提供了理论保障。  相似文献   

3.
在弹性力学问题的求解中,考虑体力的计算比考虑面力的计算要复杂很多,而且在力学实验中模拟体力的载荷条件通常也比较困难。因此,将体力转化为面力,可以简化弹性力学问题的求解,并且对于实验设计,也可提供极大的方便。本文以两个典型平面问题为例,分别探讨了在直角坐标系和极坐标系下对非常体力的处理方法,为实验的设计提供了新的思路,有助于学生灵活运用弹性力学理论解决实际工程问题,具有一定的工程应用价值和教学实践意义。  相似文献   

4.
弹性力学的一种正交关系   总被引:10,自引:2,他引:8  
罗建辉  刘光栋 《力学学报》2003,35(4):489-492
在弹性力学求解新体系中,将对偶向量进行重新排序后,提出了一种新的对偶微分矩阵,对于有一个方向正交的各向异性材料的三维弹性力学问题发现了一种新的正交关系.将材料的正交方向取为z轴,证明了这种正交关系的成立.对于z方向材料正交的各向异性弹性力学问题,新的正交关系包含弹性力学求解新体系提出的正交关系。  相似文献   

5.
提出了弹性力学三段式教学方法,即围绕每一知识点,按照工程背景、数理基础、力学原理进行划分,在教学实施中遵循先工程,后数理,再力学的讲解顺序. 工程背景可与材料力学知识点进行衔接;数理基础与高等数学、解析几何等数理课程衔接,实现知识点的迁移教学;最后利用力学原理构建弹性力学的基本理论. 以弹性力学中平衡方程的讲解为例,阐述了三段式教学方法的实施过程. 该方法对降低学生学习弹性力学中的畏难情绪,提高学习信心有一定的积极作用.  相似文献   

6.
研究等截面弯钩受力时的应力分布及承载极限问题,本文以弹性力学的曲梁问题为参考,建立了平面应力条件下的金属弯钩的力学模型,得出了弯钩应力分布解,并通过ANSYS数值模拟进行验证,得出其危险截面。基于极限变形原理、弹性极限设计原理与塑性极限设计原理,提出了等截面弯钩失效的三种准则,为工厂生产不同极限载荷下的弯钩提供了理论依据。  相似文献   

7.
哈密顿体系与弹性楔体问题   总被引:2,自引:0,他引:2  
将哈密体系引入到级坐标下的弹性力学楔体问题,利用该体系辛空间的性质,将问题化为本征值和本征向量求解上,得到了完备的解空间,从而改变了弹性力学传统的拉格朗日体系以应力函数为特征的半逆法的讨论去解决该类问题的思路,给出了一条求解该类问题的直接法。  相似文献   

8.
弹塑性变形油藏中多相渗流的数值模拟   总被引:17,自引:0,他引:17  
基于流固耦合力学理论,建立了弹性变形油藏中多相渗流的数学模型,该模型考虑了渗流与变形的耦合作用,以及注采交变载荷作下油藏多孔介质的弹性变形特征,给出了耦合数值模拟方法和算例。  相似文献   

9.
Hamilton体系下弹性力学的两个守恒律   总被引:4,自引:1,他引:3  
采用与前稍有不同的方法,将Hamilton体系引入弹性力学中,并讨论了相应的Hamilto函数的守恒性和动量守恒定律,从而丰富了弹性力学的Hamilton求解体系。  相似文献   

10.
本文应用多束纤维加强超弹性复合材料应变能函数及厚壁圆筒模型,通过有限变形弹性理论研究了正常及病态下静脉壁在静脉压及轴向预拉伸作用下的变形和应力分布等力学特性,着重分析了静脉移植后自适应变化静脉壁在动脉压下的力学特性.首先利用超弹性材料厚壁圆筒模型得到了静脉壁在静脉压下的变形方程,给出了静脉压下静脉壁的变形和应力分布曲线,讨论了静脉壁的力学特性.给出了静脉移植后,正常和自适应变化静脉壁在动脉压下的变形和应力分布曲线,讨论了静脉移植后静脉壁的力学特性及其自适应性变化.然后给出了各种病态静脉壁的变形和应力分布曲线,讨论了材料参数的变化对静脉壁力学特性的影响规律.  相似文献   

11.
This paper presents a bridging research between a modeling methodology in quantum mechanics/relativity and elasticity. Using the symplectic method commonly applied in quantum mechanics and relativity, a new symplectic elasticity approach is developed for deriving exact analytical solutions to some basic problems in solid mechanics and elasticity which have long been bottlenecks in the history of elasticity. In specific, it is applied to bending of rectangular thin plates where exact solutions are hitherto unavailable. It employs the Hamiltonian principle with Legendre’s transformation. Analytical bending solutions could be obtained by eigenvalue analysis and expansion of eigenfunctions. Here, bending analysis requires the solving of an eigenvalue equation unlike in classical mechanics where eigenvalue analysis is only required in vibration and buckling problems. Furthermore, unlike the semi-inverse approaches in classical plate analysis employed by Timoshenko and others such as Navier’s solution, Levy’s solution, Rayleigh–Ritz method, etc. where a trial deflection function is pre-determined, this new symplectic plate analysis is completely rational without any guess functions and yet it renders exact solutions beyond the scope of applicability of the semi-inverse approaches. In short, the symplectic plate analysis developed in this paper presents a breakthrough in analytical mechanics in which an area previously unaccountable by Timoshenko’s plate theory and the likes has been trespassed. Here, examples for plates with selected boundary conditions are solved and the exact solutions discussed. Comparison with the classical solutions shows excellent agreement. As the derivation of this new approach is fundamental, further research can be conducted not only on other types of boundary conditions, but also for thick plates as well as vibration, buckling, wave propagation, etc.  相似文献   

12.
弹性力学混合状态方程的弱形式及其边值问题   总被引:4,自引:1,他引:3  
丁克伟  唐立民 《力学学报》1998,30(5):580-586
导出了弹性力学混合状态方程和边界条件弱形式的统一方程,此法使函数的选择无需事先完全满足边界条件,对于各种不同的边值问题可以用统一形式处理,这使得求解弹性力学问题的形式得以扩大和统一  相似文献   

13.
A new state vector is presented for symplectic solution to three dimensional couple stress problem. Without relying on the analogy relationship, the dual PDEs of couple stress problem are derived by a new state vector. The duality solution methodology in a new form is thus extended to three dimensional couple stress. A new symplectic orthonormality relationship is proved. The symplectic solution to couple stress theory based a new state vector is more accordant with the custom of classical elasticity and is more convenient to process boundary conditions. A Hamilton mixed energy variational principle is derived by the integral method.  相似文献   

14.
In this paper, the scattering of harmonic antiplane shear waves by two finite cracks is studied using the non-local theory. The Fourier transform is applied and a mixed boundary value problem is formulated. Then a set of triple integral equations is solved using a new method, namely Schmidt's method. This method is more exact and more reasonable than Eringen's for solving this kind of problem. The result of the stress near the crack tip was obtained. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip, which can explain the problem of macroscopic and microscopic mechanics.  相似文献   

15.
唐媛  卿海 《应用力学学报》2020,(2):785-792,I0023
基于修正偶应力理论及表面弹性理论,本文提出了一种新的双曲线剪切变形梁模型,用于均匀微尺度梁的静态弯曲分析。该理论可以直接利用本构关系获得横向剪切应力,满足梁顶部和底部的无应力边界条件,避免了引入剪切修正因子。根据广义Young-Laplace方程建立了梁的内部与表面层的应力连续性条件,单一的变量场可以描述梁的位移模式。通过在位移场中考虑表面层厚度以及表面层的应力连续条件,可以使新模型能够更准确地预测微尺寸和表面能相关的尺度效应。通过Hamilton原理推导出了梁的控制方程和边界条件。应变能除了考虑经典弹性理论,还要考虑微结构效应和表面能。Navier-type的解析解适用于简支边界条件,而基于拉格朗日插值的微分求积法(DQEM)可以研究在不同边界条件下的力学响应。把该数值解与Navier方法得出的解析解作了对比,得出:微尺度梁在考虑表面能或微尺寸效应、不同载荷和梁高变化下的响应一致;当不考虑微结构相关性和表面能效应时,该模型退化为经典的欧拉梁模型。  相似文献   

16.
弹性力学的一种边界无单元法   总被引:31,自引:7,他引:24  
程玉民  陈美娟 《力学学报》2003,35(2):181-186
首先对移动最小二乘副近法进行了研究,针对其容易形成病态方程的缺点,提出了以带权的正交函数作为基函数的方法-改进的移动最小二乘副近法,改进的移动最小二乘逼近法比原方法计算量小,精度高,且不会形成病态方程组,然后,将弹性力学的边界积分方程方法与改进的移动最小二乘逼近法结合,提出了弹性力学的一种边界无单元法,这种边界无单元法法是边界积分方程的无网格方法,与原有的边界积分方程的无网格方法相比,该方法直接采用节点变量的真实解为基本未知量,是边界积分方程无网格方法的直接解法,更容易引入界条件,且具有更高的精度,最后给出了弹性力学的边界无单元法的数值算例,并与原有的边界积分方程的无网格方法进行了较为详细的比较和讨论。  相似文献   

17.
The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firstly, the basic equations for elastic thin plate are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and eigenvalues are obtained simultaneously. Finally, according to the method of eigen function expansion, the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees are developed. Since the basic elasticity equations of thin plate are only used and it is not need to select the deformation function arbitrarily. Therefore, the solution is theoretical and reasonable. In order to show the correction of formulations derived, a numerical example is given to demonstrate the accuracy and convergence of the current solution.  相似文献   

18.
ntroductionThetheoreticalframeofnon_localelasticityhasbensetup[1,2].Manyimportantresultshavebengotbyusingnon_localtheorytosol...  相似文献   

19.
By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of boundary conditions. The solutions can consider both axisymmetric and non-axisymmetric cases. Solutions based on the classical plate theory and Mindlin plate theory are also presented under the corresponding boundary conditions. Numerical results are finally presented and comparisons between the three theories are made. The project is supported by the National Natural Science Foundation of China (No. 19872060).  相似文献   

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