波纹环形板的非线性弯曲

本文应用各向异性圆板的非线性弯曲理论,研究了在集中载荷作用下具有硬中心的波纹环形板,这是文献[1—4]工作的继续。本文还利用修正迭代法,求得了一个十分精确的解析公式。此法吸收了以中心挠度作为迭代参数的摄动法和常用的逐次逼近法的优点,其计算程序简单,结果精确。该公式可直接用于工程设计中。     

NONLINEAR ANALYSIS OF A CORRUGATED CIRCULAR PLATE UNDER COMBINED LATERAL LOADING

In this paper, nonlinear bending of a corrugated circular plate with a plane central region under the combined action of uniformly distributed load and a concentrated load at the center has been investigated by using large deflection theories of isotropic and anisotropic circular plates. The quite accurate analytical solutions for rigidly as well as loosely clamped edge conditions have been obtained following the modified iteration method.     

对称圆柱正交异性层合扁球壳的非线性稳定问题

本文建立了对称圆柱正交异性层合扁球壳的大挠度理论.依据这一理论.并应用修正迭代法.我们得到了均布压力作用下具有夹紧固定边界的对称圆柱正交异性层合扁球壳的临界载荷解析解.     

On the nonlinear stability of symmetrically laminated cylindrically orthotropic shallow spherical shells

In this paper,the large deflection theory of symmetrically laminated cylindricallyorthotropic shallow spherical shells is established.Based on this theory,applying themodified iteration method,the analytic solution for critical buckling loads of the shells withrigidly clamped edges under actions of uniform pressure has been obtained.     

Nonlinear bending of simply supported symmetric laminated cross-ply rectangular plates

Based on the von Kármán-type theory of plates,nonlinear bending problems of simplysupported symmetric laminated cross-ply rectangular plates under the combined action ofpressure and inplane load are investigated in this paper.The solution which satisfies thegoverning equations and boundary conditions is obtained by using the double Fourier seriesmethod.     

Nonlinear bending of circular sandwich plates

In this paper, fundamental equations and boundary conditions of nonlinear axisymmetrical bending theory for the circular sandwich plates with a soft core are derived by means of the method of calculus of variations. Especially in the case of very thin faces, the preceding fundamental epuations and boundary conditions simplity considerably. For example, a circular sandwich plate with edge clamped but free to siip under the action of uniform lateral load is considered. A more accurate solution of this problem has been obtained by means of the modified iteration method.Notation r, ,z system of cylindrical coordinates - a radius of plate boundary - t thickness of the face - h thickness of the core - h ₀ distance from middle of thickness of lower face to middle of thickness of upper face - E Young's modulus of the face - Poisson's ratio of the face - G ₂ shear modulus of the core - D _f flexural rigidity of the face - D flexural rigidity of the plate - C shear rigidity of the plate - q uniform lateral load - u _i ,v _i ,w _{i(i=1, 2, 3)} radial, tangential and normal displacement of upper face, core and lower face, respectively - u radial displacement of the middle plane of the plate - w deflection of the middle plane of the plate - rotation of connecting line of corresponding points in middle planes of two faces - _1i , _i , _zi , _ri , _zi , _{rzi (i=1,2,3)} strains at a point of upper face, core and lower face - _ri , _i , _zi , _ri , _zi , _rzi(i=1,2,3) stresses at a point of upper face, core and lower face - _r , ₀ radial and tangential stress of the middle plane of the plate, respectively - U _i(i =1, 2, 3) strain energy of upper face, core and lower face, respectively - V work done by the external force - U total potential energy of the plate - M _r radial moment of the plate - Q _r shearing force of the plate - m radial moment of the face - stress function - dimensionless radial coordinate - k dimensionless characteristic parameter - W dimensionless deflection - W ₀ dimensionless center deflection - S _r ,S ₀ dimensionless radial and tangential stress, respectively - S _r (0),S ₀ (0) dimensionless radial and tangential stress at center, respectively - S ₀(1) dimensionless tangential stress at edge - P dimensionless uniform lateral load - A ₂,A ₃,B ₂,B ₃,a ₁,.....,a ₂, ₁, ₂,l _1,1,...l _{1 1,3},m ₁,...,m ₃₃,n ₀,₂,...n ₂₂,₆,R ₁,,...R ₃₃ auxiliary quantity - L differential operator     

均布载荷作用下开顶扁球壳的非线性稳定问题

本文利用修正迭代法研究了具有硬中心的开顶扁球壳在均布载荷作用下的轴对称非线性稳定问题,得到了临界载荷的二次近似解析公式.     

夹层圆板大挠度问题的进一步研究*

本文首次给出了在均布载荷作用下、具有滑动固定边界条件并计及表板抗弯刚度的夹层圆板的非线性问题的解.在求解非线性弯曲方程时,我们提出了修正幂级数方法.然后,把本文结果与刘人怀和施云方的结果作了比较.本文解在工程应用中可用作更精确的基础.     

复合材料层合扁球壳的非线性强迫振动

研究了考虑横向剪切的对称层合圆柱正交异性扁球壳的非线性强迫振动问题，得到了共振周期解和非共振周期解．最后，还分析了横向剪切对幅频特性曲线的影响