Iterative method for large deflection nonlinear problem of laminated composite shallow shells and plates

ＩｎｔｒｏｄｕｃｔｉｏｎＡｓｃｏｍｐｏｓｉｔｅｓａｒｅｅｘｔｅｎｓｉｖｅｌｙａｐｐｌｉｅｄｉｎｍｏｄｅｒｎｅｎｇｉｎｅｒｉｎｇｓｔｒｕｃｔｕｒｅｓａｎｄｍｅｃｈａｎｉｃｓｏｆｃｏｍｐｌｅｘｍａｔｅｒｉａｌｓｈａｓｂｅｎｈｉｇｈｌｙａｄｖａｎｃｅｄ,ｉ...     

A METHOD OF DETERMINING BUCKLED STATES OF THIN PLATES AT A DOUBLE EIGENVALUE

A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular plates at a double eigenvalue are numerically analyzed. The results show that this method is effective.     

The effect of large rotation on post-buckling of annular plates

On the basis of the axisymmetrical finite deformation theory on Rissner's plates, the post-buckling behaviour of annular plates and the effect of large rotation are qualitatively and numerically discussed by the method of the bifurcation theory.The project is supported by the National Natural Science Foundation of China     

Analysis of the large deflection dynamic plastic response of simply-supported circular plates by the “membrane factor method

Based on energy equilibrium, a new procedure called the Membrane Factor Method is developed to analyze the dynamic plastic response of plates with deflections in the range where both bending moments and membrane forces are important. The final deflection of a simply-supported circular rigid-plastic plate loaded by a uniformly distributed impulse is obtained. In comparison with other approximate solutions, the present results are found to be simpler and in better agreement with the corresponding experimental values reoorded by Florence. The project supported by a fund from the National Educational Committee.     

A nonlinear mathematical model for large deflection of incompressible saturated poroelastic beams

Nonlinear governing equations are established for large deflection of incom- pressible fluid saturated poroelastic beams under constraint that diffusion of the pore fluid is only in the axial direction of the deformed beams.Then,the nonlinear bend- ing of a saturated poroelastic cantilever beam with fixed end impermeable and free end permeable,subjected to a suddenly applied constant concentrated transverse load at its free end,is examined with the Gaierkin truncation method.The curves of deflections and bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure are shown in figures.The results of the large deflection and the small deflection theories of the cantilever poroelastic beam are compared,and the differences between them are revealed.It is shown that the results of the large deflection theory are less than those of the corresponding small deflection theory,and the times needed to approach its stationary states for the large deflection theory are much less than those of the small deflection theory.     

Thermostressed State of an Anisotropic Plate with Holes and Cracks

The thermoelastic problem for an infinite multiply connected anisotropic plate with holes and cracks in a linear heat flow is solved. The stress distribution and the stress intensity factors on heat-insulated boundaries are analyzed numerically __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 127–136, September 2005.     

Buckling and large deflection behaviors of radially functionally graded ring-stiffened circular plates with various boundary conditions

The buckling and large deflection behaviors of axis-symmetric radially functionally graded (RFG) ring-stiffened circular plates are investigated by the dynamic relaxation (DR) method combined with the finite difference discretization technique. The material properties of the constituent components of the RFG plate are assumed to vary continuously according to the Mori-Tanaka distribution along the radial direction. The nonlinear governing equations are obtained in the incremental form based on the first-order shear deformation plate theory (FSDT) and the von Karman relations for large deflection. In the buckling analysis, an external in-plane load is applied to the plate incrementally so that, in each load-step, the incremental form of the governing equations can be solved by a numerical code prepared based on the DR method. After converging the DR code in the first increment, the latter load-step is added to the previous one, and the program is repeated again. The critical buckling load is determined from the compressive load-displacement curve obtained by solving the incremental form of the governing equa- tions. Based on the present incremental form of formulation, a bending analysis can also be conducted if the whole load is applied simultaneously. Finally, a detailed parametric study is carried out to investigate the influences of various boundary conditions, grading indices, thickness-to-radius ratios, stiffener’s positions and depths on the critical buckling load, and displacements and stresses resulted from the bending analysis. It is observed that the effect of the stiffener on the results is much greater in the functionally graded plate with higher material grading indices. The results also reveal that, by increasing the depth of the stiffer, the values of ascending the critical buckling load are approximately identical for both simply supported and clamped boundary conditions.     

Uniqueness for the solutions of elastic thin plates and shallow shells as well as their contact problem with half space

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｇｏｖｅｒｎｉｎｇｅｑｕａｔｉｏｎｓｆｏｒａｎｉｎｖｅｒｔｅｄｅｌａｓｔｉｃｔｈｉｎｓｈａｌｌｏｗｓｈｅｌｌｏｎｅｌａｓｔｉｃｈａｆｓｐａｃｅｉｎｓｔａｔｉｃｂｅｎｄｉｎｇａｒｅ[1]4-Ｅｉｈｉ2ｋｗ=02=2/ｘ2 2/ｙ2,2ｋ=ｋｙ(2/ｘ2) ｋｘ(2/ｙ2),(1)Ｄｉ4ｗ 2ｋ=ｑ-ｐ,(2)ｗ(ｘ,ｙ)=λｅ 2Ｇｅ4πＧｅ(λｅ Ｇｅ)∫∫ｓｐ(ξ,η)ｄξｄη(ｘ-ξ)2 (ｙ-η)2,(3)ｗｈｅｒｅｉｎＥｑｓ.(1),(2)ａｎｄ(3),ｗ(ｘ,ｙ)ｉｓｔｈｅｄｅｆｌｅｃｔｉｏｎｏｆｔｈｅｓｈｅｌｌ,(ｘ,ｙ)ｉｓｔｈｅｍ…     

Vibration control of piezoelectric beam-type plates with geometrically nonlinear deformation

This paper presents a wavelet-based approach of deformation identification and vibration control of beam-type plates with geometrically nonlinear deflection using piezoelectric sensors and actuators. The identification is performed by transferring the nonlinear equations of identifying deflection into a system of solvable nonlinear algebraic equations in terms of the measurable electric charges and currents on piezoelectric sensors. After that, a control law of negative feedback of the identified signals of deflection and velocity is employed, and the weighted residual method is chosen to determine control voltages applied on the piezoelectric actuators. Due to that the scaling function transform is like a low-pass filter which can automatically filter out high-order signals of vibration or disturbance from the measurement and the controller employed here, this control approach does not lead to the undesired phenomenon of control instability which is generated by the spilling over of high-order signals. Finally, some numerical simulations are carried out to show the efficiency of the proposed approach.     

The global bifurcation and chaos for the coupling between longitudinal and transverse vibration of a thin elastic plate in large overall motion

This paper presents the global bifurcation and chaotic behavior for the coupling of longitudinal and transverse vibration of a thin elastic plate in large overall motion. First the parametric equations of the homoclinic orbits of such a system is obtained. Then, by using the Melnikov method and digital computer simulation. the behavior of bifurcation and chaos of this vibration system is investigated in the cases of different resonances. The obvious difference between the transverse vibration and the coupling of transverse and longitudinal vibration is also shown.The project supported by the National Natural Science Foundation of China.     

集中载荷作用下不同边界条件的弯曲厚矩形板的受迫振动

运用边界积分法研究了四边简支、两对边固定另两对边简支、四边固定三种复杂边界条件下厚矩形板的受迫振动问题,求解过程清晰,从而给出了受迫振动控制方程和挠曲面方程。通过在Matlab平台上进行数值计算,得出了图表形式的计算结果,并与有限元模拟值进行对照。研究表明,边界积分法用于求解厚矩形板的受迫振动问题的准确性,本文推导的控制方程和挠曲面方程的正确性,进而对工程实际中的各种相关问题具有一定的现实意义,也为求解此类问题提供了一种新途径,可以直接运用到工程实际中。     

A mathematical theory of materials with elastic range and the definition of back stress tensor

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｇｅｎｅｒａｌ,ｔｈｅｋｉｎｅｍａｔｉｃａｌｈａｒｄｅｎｉｎｇｂｅｈａｖｉｏｒｏｆｍａｔｅｒｉａｌｓｉｓｄｅｓｃｒｉｂｅｄｂｙａｖａｒｉａｂｌｅｃａｌｅｄｂａｃｋｓｔｒｅｓｏｒｓｈｉｆｔｔｅｎｓｏｒ．Ｉｔｓｖａｌｕｅｒｅｐ...     

On some basic principles in dynamic theory of elastic materials with voids

According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author^[1], some basic principles in dynamic theory of elastic materials with voids can be established systematically. In this paper, an important integral relation in terms of convolutions is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem in dynamic theory of elastic materials with voids, but also to derive systematically the complementary functionals for the eight-field, six-field, four-field and two-field simplified Gurtin-type variational principles. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly. The project supported by the Foundation of Zhongshan University Advanced Research Center     

A mixed problem of plane elasticity for a domain with partially unknown boundary

The paper addresses a problem of plane elasticity for a doubly connected body with outer and inner boundaries in the form of regular polygons with a common center and parallel sides. The neighborhoods of the vertices of the inner boundary are unknown equal full-strength smooth arcs symmetric about the rays coming from the vertices to the center. It is assumed that this elastic body is inserted into a hole of a rigid body, with the hole boundary coinciding with the outer boundary of the elastic body. Absolutely smooth rigid punches with rectilinear bases are pressed into all the rectilinear sections of the inner polygonal boundary of the elastic body. There is no friction between the elastic and rigid bodies. The unknown arcs are free from external stresses. Complex variable theory is used to determine the unknown arcs and the stress state of the elastic body __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 110–118, March 2006.