摘要
结构稳定性临界力的计算,通常需要求解非线性超越方程组,常用的方法无法求得解析解。文中提出了一种计算压杆稳定临界力的连续分段独立一体化积分法。首先采用杆-梁比拟法建立具有四阶导数的挠度微分方程,独立积分4次,得到挠度的通解,再根据边界条件和连续性条件确定积分常数,得到挠度的解析表达式;然后根据最小能量原理得到临界力的一次近似解析解,再根据渐近法求解精确的压杆稳定微分方程得到更精确的挠度解析函数表达式,根据最小能量原理求得临界力的精确表达式。工程实例表明,连续分段独立一体化积分法编程程式化,可以得到压杆稳定临界力的最优解析解。
To calculate the critical force for structural stability,it’s usually necessary to solve the non-linear transcendental equations.It’s normally impossible to solve the analytical solution with common methods.The paper puts forward a continuous piecewise independent integral method to calculate the critical force for structural stability.First,the member-beam analogue method is used to establish the deflection differential equation with fourth order derivative,with independent integration for four times to get the general solution of the deflection.The boundary conditions and continuous conditions are used to determine the integration constant,hence to get the analytical expression for the deflection;then based on the minimum energy principle,the first-order approximate analytical solution is solved for the critical force.The precise compressionbar stability differential equation is solved with the approximation method to get the more precise deflection analytic function expression.The precise expression is solved based on the minimum energy principle.The engineering practices show that the continuous piecewise independent integral method is programmable,which can be used to get the optimal analytical solution for the critical force for structural stability.
出处
《起重运输机械》
2015年第9期36-42,共7页
Hoisting and Conveying Machinery
基金
国家自然科学基金资助项目(10632040)
关键词
稳定性调整
快速解析法
最小能量原理
渐近法
定性判断法
stability adjustment
fast analytical research
minimum energy theory
approximation method
qualitative judgment method
