The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. T...The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. The formulation is based on the assumption that the flexural rigidity of the plate varies in the plane following a power form, and Poisson＇s ratio is constant. A fourth-order partial differential equation with variable coefficients is derived by assuming a Levy-type form for the transverse displacement. The governing equation can be transformed into a Whittaker equation, and an analytical solution is obtained for a thin rectangular plate subjected to the distributed loads. The validity of the present solution is shown by comparing the present results with those of the classical solution. The influence of in-plane variable stiffness on the deflection and bending moment is studied by numerical examples. The analytical solution presented here is useful in the design of rectangular plates with in-plane variable stiffness.展开更多
Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or pa...Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or particle scale mechanical analyses of these systems. The electrostatic repulsive force depends on the mid-plane potential between two charged particles. Previous analytical solutions of the mid-plane potential, including those based on simplified assumptions and modern mathematic methods, are reviewed. It is shown that none of these solutions applies to wide ranges of interparticle distance from 0 to 10 and surface potential from 1 to 10. Three previous analytical solutions are chosen to develop a semi-analytical solution which is proven to have more extensive applications. Furthermore, an empirical closed-form expression of mid-plane potential is proposed based on plenty of numerical solutions. This empirical solution has extensive applications, as well as high computational efficiency.展开更多
A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a fl exible wall on a rigid shallow circular foundation embedded in an elastic half-space is pr...A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a fl exible wall on a rigid shallow circular foundation embedded in an elastic half-space is presented. This research generalizes the previous solution by Trifunac in 1972, which tackled only the semi-circular foundation, to arbitrary shallow circular-arc foundation cases, and is thus comparatively more realistic. Ground surface displacement spectra at higher frequencies are also obtained. As an analytical series solution, the accuracy and error analysis of the numerical results are also discussed. It was observed from the results that the rise-to-span ratio of the foundation profi le, frequency of incident waves, and mass ratios of different media(foundation-structure-soil) are the three primary factors that may affect the surface ground motion amplitudes near the structure.展开更多
基金Supported by the Ministry of Research,Technology,and Higher Education Republic of Indonesia,through the Budget Implementation List(DIPA)of Diponegoro University,Grant No.DIPA-023.04.02.189185/2014,December 05,2013
文摘优化分析和计算液体动力学(CFD ) 同时被使用了，在哪个一个参量的模型在发现最佳的答案起一个重要作用。然而，与不规则的曲线为复杂形状创造一个参量的模型是困难的，例如一种海底的壳形式。在这研究，立方的 Bezier 曲线和曲线飞机交叉方法被用来产生考虑三个输入参数的一种参量的海底的壳形式的一个稳固的模型：鼻子半径，尾巴半径，和长度高度壳比率(L/H ) 。应用程序接口(API ) 脚本也被用来在 ANSYS 设计 modeler 写代码。结果证明海底的形状能与输入参数的某变化被产生。一个例子被给那显示出建议方法怎么能成功地被用于一个壳抵抗优化盒子。中间的海底的类型的参量的设计被选择被修改。首先，预先，原来的海底的模型用 CFD 被分析。然后，使用反应表面图，某候选人有一个最小的壳抵抗系数的最佳的图案被获得。进一步，在目标驱动的优化(GDO ) 的优化方法被实现与最小的壳抵抗系数发现海底的壳形式(C <sub> t </sub>) 。最小的 C <sub> t </sub> 被获得。在在起始的潜水艇和最佳潜水艇之间的 C <sub> t </sub> 价值的计算差别在 0.26% 附近，与起始的潜水艇和是的最佳潜水艇的 C <sub> t </sub> 0.001 508 26 和 0.001 504 29 分别地。结果证明最佳潜水艇壳形式显示出更高的鼻子半径(r <sub> n </sub>) 和更高的 L/H 起始的潜水艇比那些塑造，当时尾巴的半径(r <sub> t </sub>) 比起始的形状的小。
基金Project supported by the National Natural Science Foundation of China (No. 11072177)
文摘The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. The formulation is based on the assumption that the flexural rigidity of the plate varies in the plane following a power form, and Poisson＇s ratio is constant. A fourth-order partial differential equation with variable coefficients is derived by assuming a Levy-type form for the transverse displacement. The governing equation can be transformed into a Whittaker equation, and an analytical solution is obtained for a thin rectangular plate subjected to the distributed loads. The validity of the present solution is shown by comparing the present results with those of the classical solution. The influence of in-plane variable stiffness on the deflection and bending moment is studied by numerical examples. The analytical solution presented here is useful in the design of rectangular plates with in-plane variable stiffness.
基金Project supported by the National Key Basic Research Program of China(Grant No.2012CB026103)the National Natural Science Foundation of China(Grant No.51009136)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2011212)
文摘Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or particle scale mechanical analyses of these systems. The electrostatic repulsive force depends on the mid-plane potential between two charged particles. Previous analytical solutions of the mid-plane potential, including those based on simplified assumptions and modern mathematic methods, are reviewed. It is shown that none of these solutions applies to wide ranges of interparticle distance from 0 to 10 and surface potential from 1 to 10. Three previous analytical solutions are chosen to develop a semi-analytical solution which is proven to have more extensive applications. Furthermore, an empirical closed-form expression of mid-plane potential is proposed based on plenty of numerical solutions. This empirical solution has extensive applications, as well as high computational efficiency.
文摘A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a fl exible wall on a rigid shallow circular foundation embedded in an elastic half-space is presented. This research generalizes the previous solution by Trifunac in 1972, which tackled only the semi-circular foundation, to arbitrary shallow circular-arc foundation cases, and is thus comparatively more realistic. Ground surface displacement spectra at higher frequencies are also obtained. As an analytical series solution, the accuracy and error analysis of the numerical results are also discussed. It was observed from the results that the rise-to-span ratio of the foundation profi le, frequency of incident waves, and mass ratios of different media(foundation-structure-soil) are the three primary factors that may affect the surface ground motion amplitudes near the structure.
