CAJ | 학술논문

传统配点法在求解动力学问题时会存在误差随时间累积的问题，而无网格径向基函数配点法在全域内采用具有无限连续性的径向基函数作为近似函数，结合配点法构建方程，通过最小二乘法进行求解。无网格径向基函数配点法不仅在数值计算过程中不需要任何网格，是真正的无网格法，而且易于离散，精度高，不需要积分，计算效率高；径向基函数的近似函数仅与距中心点的距离有关，非常适宜于求解三维问题。对于这种方法，本文先离散空间域，然后再离散时间域，并在每一时间步内施加边界条件，来分析三维功能梯度材料板的静力和动力问题，据此可解决传统配点方法在求解动力问题时误差随时间累积的问题。数值分析表明，材料性能呈梯度分布会导致其力学性能在梯度方向呈现非线性变化，不同的梯度分布模式会导致力学性能非线性变化的幅度不同。
전통배점법재구해동역학문제시회존재오차수시간루적적문제，이무망격경향기함수배점법재전역내채용구유무한련속성적경향기함수작위근사함수，결합배점법구건방정，통과최소이승법진행구해。무망격경향기함수배점법불부재수치계산과정중불수요임하망격，시진정적무망격법，이차역우리산，정도고，불수요적분，계산효솔고；경향기함수적근사함수부여거중심점적거리유관，비상괄의우구해삼유문제。대우저충방법，본문선리산공간역，연후재리산시간역，병재매일시간보내시가변계조건，래분석삼유공능제도재료판적정력화동력문제，거차가해결전통배점방법재구해동력문제시오차수시간루적적문제。수치분석표명，재료성능정제도분포회도치기역학성능재제도방향정현비선성변화，불동적제도분포모식회도치역학성능비선성변화적폭도불동。
Meshfree radial basis collocation method (RBCM)is introduced to study the static and dynamic problems of the three dimensional (3D)functionally graded plate.Radial basis functions which possess infinite continuity are employed to be the ap-proximation,collocation method is utilized for discretization,and least squares approach is adopted to solve the discretized equa-tions .No mesh will be required in the discretization and resolution and therefore RBCM is a truly meshfree method.Discretization scheme of RBCM is quite simple and high accuracy can be obtained.Radial basis approximation only depends on the distance from the center which makes RBF a good candidate to solve 3D problems.Conventional collocation method introduces error accumula-tion on the boundaries.In this paper,the spatial domain is discretized first,and then temporal domain is discretized.Boundary conditions are imposed in each time step.Therefore,error accumulation on the boundaries can be overcome.Numerical simula-tions demonstrate that graded distribution of material properties will lead to nonlinear variation of the mechanical properties.The magnitude of the nonlinear variation will be different for different graded distributions.