共查询到19条相似文献,搜索用时 250 毫秒
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通过引入三个标量函数,结合Fourier变换,首先将横观各向同性饱和多孔半空间的基本方程组简化为一个6阶控制方程和一个2阶控制方程;求解这两个控制方程,给出了横观各向同性饱和多孔半空间相关物理量的解析表达式.利用带扩展项的正弦级数解答,在将梁下地基表面沉降也展成正弦级数后,结合板-地基的相容条件(连续条件),对横观各向同性饱和多孔半空间与有限长梁的动力相互作用问题进行了分析、计算.另外,利用Fourier变换,对横观各向同性饱和多孔半空间与无限长梁的动力相互作用问题进行了分析. 相似文献
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选用弹性半空间地基模型分析四边自由各向异性矩形地基板的弯曲和稳态振动解析解。将异性薄板控制微分方程与基于弹性半空间地基位移解建立的板与地基变形协调方程相结合,先按对称性分解,然后采用三角级数法得出了弹性半空间地基上四边自由各向异性矩形薄板的弯曲和稳态振动解析解,包括地基反力(幅值)、板的挠度(幅值)、板的内力(幅值)的解析表达式。克服了数值法的弊端,取消了对地基反力的假设,得到了板的内力(幅值)及地基反力(幅值)更切实际的分布规律。算例结果不但与文献结果吻合良好,而且表明对于异形板,对称载荷能引起反对称的内力和变形。该方法使得半空间地基上各向异性矩形薄板这一复杂的接触问题的求解统一化、简单化、规律化。 相似文献
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选用弹性半空间地基模型分析四边自由各向异性矩形地基板的弯曲和稳态振动解析解。将异性薄板控制微分方程与基于弹性半空间地基位移解建立的板与地基变形协调方程相结合,先按对称性分解,然后采用三角级数法得出了弹性半空间地基上四边自由各向异性矩形薄板的弯曲和稳态振动解析解,包括地基反力(幅值)、板的挠度(幅值)、板的内力(幅值)的解析表达式。克服了数值法的弊端,取消了对地基反力的假设,得到了板的内力(幅值)及地基反力(幅值)更切实际的分布规律。算例结果不但与文献结果吻合良好,而且表明对于异形板,对称载荷能引起反对称的内力和变形。该方法使得半空间地基上各向异性矩形薄板这一复杂的接触问题的求解统一化、简单化、规律化。 相似文献
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考虑路面板和地基的相互作用,将路面板作为三维弹性体,建立路面板-层状多相弹性地基动力响应的三维多相层状弹性半空间体模型,分析了移动荷载作用下路面板-多相弹性地基系统的动力响应.将移动单元法引入到两相饱和弹性介质的半解析方法中,构造了随荷载按照相同速度运动的移动层单元,基于移动坐标下两相饱和弹性介质的动力控制方程和边界条件,应用加权残数法建立了两相弹性介质移动层单元动力方程,该方程可退化为单相弹性介质移动层单元动力方程,基于此,建立了移动荷载下多相弹性地基与路面板系统的三维动态响应的统一的半解析方程.并以两相饱和弹性半空间地基-单相弹性地基-路面板所形成的路面结构为例,数值分析了荷载速度、饱和层渗透系数、弹性层厚度等参数对路面板位移和土体孔压响应的影响.研究结果表明移动单元法是研究移动荷载下路面结构动态响应的一种有效的方法. 相似文献
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提出了功能梯度圆板在轴对称载荷作用下的简化理论与解析解. 引入了板理
论的若干假设(Kirchhoff假设的一部分,Reissner-Mindlin假设和文中提出的假设),并假
设材料常数在板厚方向按指数规律变化. 推导了板的周边固定或简支同时又接地情况下中性
层法线转角的解和用Fourier-Bessel级数表示的电势解. 这个解在形式上比精确解简单得
多,进行数值计算时也相当方便与快捷. 该文给出了板的周边固定、接地情况下的计算结果
并进行了讨论,对于理论和方法的正确性作了验证. 相似文献
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Axisymmetric bending of functionally graded circular magneto-electro-elastic plates of transversely isotropic materials is analyzed based on linear three-dimensional theory of elasticity coupled with magnetic and electric fields. The transverse loads are expanded in Fourier-Bessel series and therefore can be arbitrarily distributed along the radial direction. The radial distributions of the displacements are assumed in combination of Fourier-Bessel series and polynomials as well as the electric potential and magnetic potential. If the material properties obey the exponential law along the thickness of the plate, two three-dimensional exact solutions for two unusual boundary conditions can be derived since they satisfy the governing equations and specified boundary conditions point by point. For simply supported or clamped boundary, the obtained solutions satisfy the governing equations exactly and the boundary conditions approximately. A layer wise model is also introduced to treat with the plates whose material property components vary independently and arbitrarily along the thickness of the plates. The numerical results are finally tabulated and plotted to demonstrate the presented method and agree well with those from finite element methods. 相似文献
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In this paper a solution of deflection in the form of Fourier-Bessel double series with supplementary terms is proposed to analyse bending and vibration problems of thin elastic sector plate with various edge conditions. This solution is suitable to a wider range, convenient for calculation and it is in an analytical form. As computational examples, the distribution curves of deflection and bending moment of plates with various sector angles, simply supported or clamped along the radial edges under uniform or concentrated load are obtained and the result are compared with the numerical results of related references. Thus the range of application of the Fourier series method with supplementary terms is extended. Frequencies and nodal lines in free vibration of plates with various sector angles simply supported along the radial edges are also given in this paper.Communicated by Hsueh Dai-wei. 相似文献
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圆弧形层状沉积谷地对入射平面SV波散射解析解 总被引:10,自引:0,他引:10
利用Fourier—Bessel级数展开法给出了圆弧形层状沉积谷地对入射平面SV波散射问题的一个解析解,并分析了谷中层状沉积排列顺序及相对刚度等因素对散射的影响. 相似文献
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In this paper, 3-dimensional non-axisymmetrical deformation analyses for finite hollow circular cylinders have been carried
out by Pickett's double series expansion method[1]. Through expanding the displacement potentials as the sum of fourier series and Fourier-Bessel series, we could express the
coefficients of one series by those of another under certain boundary conditions. Thus, a set of linear algebraic equations
were derived. Solving these equations, we could obtain the solutions of the problems. Numerical examples have been given to
show that the method presented here is workable for practical applications. 相似文献
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The present paper investigates the basic characteristics of the interlaminar stresses in a double-layer cylindrical shell with both ends simply-supported under uniform external or internal pressure. The double layer shell is composed of a 0° fiber-reinforced composite layer and an isotropic layer. In this paper, this axisymmetric problem is solved exactly with the three-dimensional theory of elasticity. Both the displacement field and the stress field of each layer of the shell are expressed in Fourier series and Fourier-Bessel series. Then we illustrate the effects of the various parameters, such as geometry, material constants, loading conditions and stacking sequence, on the interlaminar stresses. 相似文献
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圆弧形凹陷地形表面覆盖层对入射平面P波的影响 总被引:15,自引:0,他引:15
利用Fourier-Bessel级数展开法给出了表面具有覆盖层的圆弧形凹陷地形对入射平面P波散射问题的一个解析解,并利用该解分析了不同形状凹陷地形表面覆盖层刚度和厚度对入射P波的影响。结果表明,凹陷地形表面覆盖层的存在,即使厚度很薄,对入射P波的散射也具有很大覆盖,覆盖层刚度和厚度的变化可显著改善凹陷地形场地的动力特性。 相似文献
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将波函数展开法与奇异积分方程技术相结合研究了平面波对有部分脱胶衬砌的圆形孔洞的散射。将脱离区看作弧形裂纹并忽略裂纹表面的相互作用。将衬砌和基体中的波场展开成Fou-rier-Bessel级数,利用混合边界条件得到一组对偶级数方程组并进一步转化成Hilbert奇异积分方程。数值求解给出了脱离区大小和衬砌厚度对动应力强度因子(DSIF)和散射截面(SCS)的影响。结果显示由于脱胶,动应力强度因子和散射截面呈现明显的低频共振特性。 相似文献