Closed-form Analytical Solution for Beam on Elastic Foundation with Different Tension and Compression Modulus

On the basis of the theory of different modulus, the closed-form analytical solution for beams on elastic foundations with different modulus has been derived. A comparison is made between the results of the analytical solution and those calculated from the classic mechanic theories, in which the tension modulus are equal to the compression modulus. It is shown from the numerical results that the ratio of compressive modulus to tensile modulus will greatly affect the elastic characteristic values,internal forces and flexibilities. The present theory satisfies the mechanical behavior of materials. The amount of materials can be economized through rational design by using the elastic theory of different modulus.     

一类6-SPS相似平台并联机构正运动学的简明解

6-SPS相似 Stewart平台是一种动、静平台均为平面六边形 ,且彼此相似的并联机构。并联机构正运动学是一个位置和姿态耦合的复杂非线性问题 ,难以求得解析解。通过引入四元数来表示旋转变换和应用对偶空间方法对高阶多项式进行降阶处理 ,可以用一组二阶方程来表示该类并联机构的正运动学。在这组方程中 ,动平台的位置和姿态是解耦的。此外 ,在方程组求解过程中 ,能避免产生伪复根。最后通过求根公式直接得到机构动平台位姿的 8个解析解