针对薄板非线性迭代计算量很大的问题,依据von Kárman薄板非线性理论构造能量泛函,并用数值积分和数值微分进行离散,得到非线性方程组,从而利用求积元法(Quadrature Element Method,QEM)求解薄板的中等挠度的弯曲和非线性屈曲问题...针对薄板非线性迭代计算量很大的问题,依据von Kárman薄板非线性理论构造能量泛函,并用数值积分和数值微分进行离散,得到非线性方程组,从而利用求积元法(Quadrature Element Method,QEM)求解薄板的中等挠度的弯曲和非线性屈曲问题,得到可信的结果.算例表明:在处理薄板几何非线性问题上,QEM计算效率很高,应用潜力很大.展开更多
This paper is concerned with the effects of boundary conditions on the large-amplitude free vi-brations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported en...This paper is concerned with the effects of boundary conditions on the large-amplitude free vi-brations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail. Given a spe-cific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC. It is found that the slenderness ratio has a significant influence on the nonlinear frequency. For slender beams, the nonlinear effects of bending curva-ture and shear strain are negligible regardless of the boundary conditions. For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC.展开更多
The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method （QEM） is use...The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method （QEM） is used for the vibration analysis. The fundamental frequencies of beams are presented for various slenderness ratios and nonlinear foundation parameters for both slender and short beams. The results for slender beams compare well with finite element results. The analysis shows that the transverse shear deformation and the nonlinear foundation parameter significantly affect the fundamental frequency of the beams.展开更多
The triangular differential quadrature method was used to analyze the free vibrations of moderately thick sectorial plates. A triangular serendipity transformation was introduced to map the sectorial domain onto a uni...The triangular differential quadrature method was used to analyze the free vibrations of moderately thick sectorial plates. A triangular serendipity transformation was introduced to map the sectorial domain onto a unit isosceles right triangle. The first six non-dimensional frequencies of the sectorial plates were obtained for various combinations of clamped and simply supported boundary conditions. For sectorial plates with simply supported radial edges, the present results agree well with the available exact solutions and finite element solutions, demonstrating the effectiveness of the method.展开更多
文摘针对薄板非线性迭代计算量很大的问题,依据von Kárman薄板非线性理论构造能量泛函,并用数值积分和数值微分进行离散,得到非线性方程组,从而利用求积元法(Quadrature Element Method,QEM)求解薄板的中等挠度的弯曲和非线性屈曲问题,得到可信的结果.算例表明:在处理薄板几何非线性问题上,QEM计算效率很高,应用潜力很大.
基金Supported by Basic Research Foundation of Tsinghua University (No. JC2001003)
文摘This paper is concerned with the effects of boundary conditions on the large-amplitude free vi-brations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail. Given a spe-cific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC. It is found that the slenderness ratio has a significant influence on the nonlinear frequency. For slender beams, the nonlinear effects of bending curva-ture and shear strain are negligible regardless of the boundary conditions. For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC.
基金Supported by the Tsinghua Fundamental Research Foundation (No. JCXX2005069)the National Natural Science Foundation of China (No. 50778104)
文摘The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method （QEM） is used for the vibration analysis. The fundamental frequencies of beams are presented for various slenderness ratios and nonlinear foundation parameters for both slender and short beams. The results for slender beams compare well with finite element results. The analysis shows that the transverse shear deformation and the nonlinear foundation parameter significantly affect the fundamental frequency of the beams.
文摘The triangular differential quadrature method was used to analyze the free vibrations of moderately thick sectorial plates. A triangular serendipity transformation was introduced to map the sectorial domain onto a unit isosceles right triangle. The first six non-dimensional frequencies of the sectorial plates were obtained for various combinations of clamped and simply supported boundary conditions. For sectorial plates with simply supported radial edges, the present results agree well with the available exact solutions and finite element solutions, demonstrating the effectiveness of the method.
