【作者】 平学成；

【导师】 谢基龙； 陈梦成；

【作者基本信息】 北京交通大学 ， 车辆工程， 2006， 博士

【摘要】 各向异性材料和压电材料常常单独或与其它材料接合使用，材料中的裂纹、V型切口和夹杂角尖等部位均存在奇异性，很可能导致部件的功能失效和早期破坏。为了确保设备和结构的安全可靠性，全面准确地了解这些部位的奇异性场强度有着非常重要的意义。通常奇异性场可统一表示为∑(r，θ)=kr~λF(θ)，其中(r，θ)为原点设在奇异点的极坐标，特征值λ和特征角分布函数F(θ)为特征解，k为强度系数。为了确定奇异性场强度和建立断裂准则，不但要求解特征解，而且要确定强度系数k，为此，本文建立了几类新型奇异性单元，并与全域杂交元结合，用来求解各向异性材料和压电材料奇异性场强度。奇异单元建立的思路为：利用高次内插有限元特征法求解奇异性场的特征解，并以此为基础，通过广义Hellinger-Reissner变分原理建立围绕奇异点邻域的超级奇异性单元。将超级奇异单元与全域杂交元结合，用来求解各向异性材料和压电材料奇异性场强度。根据材料和结构形式的不同，主要包含以下研究内容： 1)建立各向异性材料裂纹尖端超级奇异单元，用于求解各向异性接合材料裂纹尖端场强度，确定应力强度因子的数值解。文中通过算例验证所建立的模型，并考察材料主轴走向、裂纹长度、裂纹间距、材料属性和结构形式等的影响。 2)建立面内极化压电材料的裂纹尖端超级奇异单元，用于求解奇异性电弹场强度。该单元考虑的裂纹面电边界条件包括：绝缘条件、部分导通条件和导通条件。通过典型算例，对方法进行了验证，并分析了各种电边界条件和极化方向等对应力和电位移强度因子的影响。 3)建立面外极化压电材料界面裂纹尖端超级奇异单元，用于求解层间裂纹的应力和电位移强度。考虑的接合材料种类包括：压电／压电、压电／弹性绝缘体以及压电／弹性导体。通过算例考察了电边界条件，层厚和外载等因素对强度因子和能量释放率的影响。 4)建立各向异性材料和压电材料超级界面端单元，用于求解接合材料界面端部的奇异性场强度。通过算例分析，考察了材料主轴走向，界面端角度，材料属性和结构尺度对应力强度和电位移强度的影响。 5)建立了各向异性材料和压电材料超级夹杂角尖单元，用于求解该处的奇异性场强度。算例考虑了夹杂角尖角度、夹杂尺寸和夹杂间距等的影响，据此判断界面的安全性。更多还原

【Abstract】 Anisotropic materials and piezoelectric materials are often used by oneself or bonded with other materials. Unfortunately, strong singularities in the tips of the cracks, interface edges and inclusions may lead to function invalidation or even earlier destroy of components. To ensure the safety and reliability of the devices and structures, it is meaningful to understand completely and exactly the local singular fields. Commonly, the singular fields surrounding the singular points can be expressed as ∑ = k r~λ F(θ), in which (r,θ) is the polar coordinate system whose origin is set at the singular point, eigenvalue X and angular variation function F(θ) are eigensolutions, k is the magnified coefficient depending on the given loading, the geometry of the structure and material constants. To determine the singular fields and the fracture parameters, both the eigensolutions and the magnified coefficients should be solved. The main objective of this dissertation is to establish several kinds of super singular elements, and combine them with the standard hybrid element to solve the singular fields of anisotropic and piezoelectric materials. To establish the super singular elements, two steps are needed: Firstly, the eigensolutions of singular fields in the crack-tips of anisotropic materials are solved by a kind of ad hoc finite element eigenanalysis method; Secondly, based on generalized Hellinger-Reissner variational functional, a kind of super crack-tip singular element is established. In terms of materials and geometries in the researches, the main contents are described as following:1) A kind of super crack-tip singular element is developed to investigate the singular fields around the crack-tips of bonded anisotropic materials, and the numerical solutions of stress intensity factors (SIFs) are obtained by the solved singular stresses. The new model is verified with avaible solutions. Other new numerical results are also given to investigate the influences of fibre orientation, cracks length, crack distances, material mismatches and material geometry.2) A kind of super crack-tip element model is developed to investigate the singular electro-elastic fields around the crack-tips of inplane polarized piezoelectric materials, in which three kind of boundary conditions, i.e., impermeable condition, limited permeable and更多还原