CAJ | 학술논문

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。
결구은정성림계력적계산，통상수요구해비선성초월방정조，상용적방법무법구득해석해。문중제출료일충계산압간은정림계력적련속분단독립일체화적분법。수선채용간－량비의법건립구유사계도수적뇨도미분방정，독립적분4차，득도뇨도적통해，재근거변계조건화련속성조건학정적분상수，득도뇨도적해석표체식；연후근거최소능량원리득도림계력적일차근사해석해，재근거점근법구해정학적압간은정미분방정득도경정학적뇨도해석함수표체식，근거최소능량원리구득림계력적정학표체식。공정실례표명，련속분단독립일체화적분법편정정식화，가이득도압간은정림계력적최우해석해。
To calculate the critical force for structural stability,it’s usually necessary to solve the non-linear tran-scendental equations.It’s normally impossible to solve the analytical solution with common methods.The paper puts for-ward 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 in-dependent 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 compression-bar stability differential equation is solved with the approximation method to get the more precise de-flection analytic function expression.The precise expression is solved based on the minimum energy principle.The engi-neering 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.