The Solving Problem and the Difference Solving Process for the Shear of a Bonded Elastic Bodies
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摘要: 两刚性平行平面之间粘附长条弹性体(其横截面为矩形),在上下两面相反方向切向力的作用下,弹性体将发生变形.在导出这种变形的数学模型的基础上,给出了一种新的差分解法.对于具有奇性的边界条件,进行了详细的分析和推导,给出了一种合理而有效的新的离散边界条件.模拟计算表明,其结果与定性分析相吻合.因此对该类问题的研究提供了新的实用的数值解法和数值分析方法.Abstract: A long elastomer with rectangular section bonded between two parallel rigid surfaces will come about deformation because of the role of two opposite shear forces in both the top and bottom plate.The mathematic model of the deformation is deduced and a new difference solving process is proposed.For boundary condition with singularity,a detailed analysis and deduction is given and a new rational and effective discrete boundary condition is proposed.Simulate computation demonstrates that the result is identical with qualitative analysis.Therefore,a new and functional numerical method and quantitative analysis method are provided.
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Key words:
- elastic body /
- shear /
- mathematic model /
- difference scheme
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[1] Gent A N.Meinecke E A.Compression bending and shearing of bonded rubber blocks[J].Polymer Engineering and Science,1970,10(1):48～53. [2] Lindley P B.A finite-element programme for the plane-strain analysis of rubber[J].J Strain Analysis,1975,10(1):25～31. [3] Lindley P B,Teo S C.Some numerical stiffnesses of soft elastic blocks bonded to rigid end plates[J].Plastics and Rubber Mat Appl,1978,8:113～116. [4] Haddow J B,Ogden R W.Compression of bonded elastic bodies[J].J Mech Phys Solids,1988,36(5):551～579. [5] 徐秉业,刘信声.应用弹塑性力学[M].北京:清华大学出版社,1995,382～384. -
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