Axisymmetrical Nonlinear Bending and Buckling of a Circular Plate Under Large Load

With the terms of the exact series solution taken as trial functions, the method of point collocation was used to calculate the large deflection of a circular plate. The axisymmetrical bending formulae were developed for the calculation of a circular plate subjected to polynomial distributed loads, a concentrated load at the center, uniform radial forces and moments along the edge or their combinations. The support may be elastic. The buckling load was calculated. Under action of uniformly distributed load, central load or their compound load, solutions were compared with those obtained by other methods, Buckling beyond critical thrust was compared with that calculated by the power series method. The method presented in this paper has advantages of wide convergent range, high precision and short computing time. Moreover, the computing time is nearly independent of the complexity of the loads.     

Nonlinear vibration of circular plate with variable thickness

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Nonlinear Analysis and Optimization of Shallow Shells of Variable Thickness

NomenclaturelintroductionWiththerapiddevelopmelltinshellanalysis,flexibleshellshavefoundWiderapplicationsinengineering.Muchattentionisculal.entlyfoctlsedonthenonlinearbendingandstabilityproblemsofthoseshells.Thebehaviorofflexibleshellsisgovernedbynonlinea…     

Hierarchical closed form solutions for plates bent by localized transverse loadings

3D and 2D closed form plate models are here applied to static analysis of simply supported square isotropic plates. 2D theories are hierarchically classified on the basis of the accuracy of the displacements and stresses obtained by comparison to the 3D exact results that could be assumed by the reader as benchmark for further analyses. Attention is mainly paid on localized loading conditions, that is, piecewise constant load. Also bi-sinusoidal and uniformly distributed loadings are taken into account. All of those configurations are considered in order to investigate the behavior of the 2D models in the case of continu- ous/uncontinuous, centric or off-centric loading conditions. The ratio between the side length a and the plate thickness h has been assumed as analysis parameter. Higher order 2D models yield accurate results for any considered load condition in the case of moderately thick plates, a/h=10. In the case of thick plates, a/h=5, and continuous/uncontinuous centric loading conditions high accuracy is also obtained. For the considered off-centric load condition and thick plates good results are provided for some output quantities. A better solution could be achieved by simply increasing the polynomial approximation order of the axiomatic 2D displacement field.     

Hierarchical models for failure analysis of plates bent by distributed and localized transverse loadings

The failure analysis of simply supported, isotropic, square plates is addressed. Attention focuses on minimum failure load amplitudes and failure locations, von Mises＇ equivalent stress along the plate thickness is also addressed. Several distributed and localized loading conditions are considered. Loads act on the top of the plate. Bi-sinusoidal and uniform loads are taken into account for distributed loadings, while stepwise constant centric and off-centric loadings are addressed in the case of localized loadings. Analysis is performed considering plates whose length-to-thickness ratio a/h can be as high as 100 （thin plates） and as low as 2 （very thick plates）. Results are obtained via several 2D plate models. Classical theories （CTs） and higher order models are applied. Those theories are based on polynomial approximation of the displacement field. Among the higher order theories （HOTs） HOTsa models account for the transverse shear deformations, while HOTs models account for both transverse shear and transverse normal deformations. LHOTs represent a local application of the higher order theories. A layerwise approach is thus assumed： by means of mathematical interfaces, the plate is considered to be made of several fictitious layers. The exact 3D solution is presented in order to determine the accuracy of the results obtained via the 2D models. In this way a hierarchy among the 2D theories is established. CTs provide highly accurate results for a/h greater than 10 in the case of distributed loadings and greater than 20 for localized loadings. Results obtained via HOTs are highly accurate in the case of very thick plates for bi-sinusoidal and centric loadings. In the case of uniform and off-centric loadings a high gradient is present in the neighborhood of the plate top. In those cases, LHOTs yield results that match the exact solution.     

Exact free vibration analysis of open circular cylindrical shells by the method of reverberation-ray matrix

This paper is concerned with the free vibration analysis of open circular cylindrical shells with either the two straight edges or the two curved edges simply supported and the remaining two edges supported by arbitrary classical boundary conditions. Based on the Donnell-Mushtari-Vlasov thin shell theory, an analytical solution of the traveling wave form along the simply supported edges and the modal wave form along the remaining two edges is obtained. With such a unidirectional traveling wave form solution, the method of the reverberation-ray matrix is introduced to derive the equation of natural frequencies of the shell with different classical boundary conditions. The exact solutions for natural frequencies of the open circular cylindrical shell are obtained with the employment of a golden section search algorithm. The calculation results are compared with those obtained by the finite element method and the methods in the available literature. The influence of length, thickness, radius, included angle, and the boundary conditions of the open circular cylindrical shell on the natural frequencies is investigated. The exact calculation results can be used as benchmark values for researchers to check their numerical methods and for engineers to design structures with thin shell components.     

Theoretical Calculation and Analysis of Slip and Deformation for Concrete Sandwich Panels

Slip and deformation of concrete sandwich panels under uniformly distributed loads is concerned. The effect of slip on the deformation of concrete sandwich panels are studied,and the analytical expressions of slip and deformation for concrete sandwich panels is obtained. These formulae can describe the slip distribution and account for its effect on deformation. In order to restrict the bound of formula, the formula of crack moment is obtained. The results of theoretical calculation are compared with those of tests and finite element methods. The comparison shows that the results of theoretical calculation are in accord with those of tests and finite element methods. So the theoretical calculation can be used to calculate slip and deformation of concrete sandwich panels in practical projects.     

Analytical solutions of simply supported magnetoelectroelastic circular plate under uniform loads

INTRODUCTIONInelasticity ,theproblemofasimplysup portedcircularplatesubjectedtouniformloadsisaclassicone .Timoshenkoetal.(1970 )pre sentedasolutionforanisotropiccircularplate .Dingetal.(2 0 0 0 ;2 0 0 1)obtainedtheanalyti calthree dimensionalsolutionforat…     

Analytical solution for functionally graded anisotropic cantilever beam under thermal and uniformly distributed load

The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.     

Analytical solutions of simply supported magnetoelectroelastic circular plate under uniform loads

In this paper, the axisymmetric general solutions of transversely isotropic magnetoelectroelastic media are expressed with four harmonic displacement functions at first. Then, based on the solutions, the analytical three-dimensional solutions are provided for a simply supported magnetoelectroelastic circular plate subjected to uniform loads. Finally, the example of circular plate is presented. Project supported by the National Natural Science Foundation of China (No. 10172075) and Ningbo Natural Science Foundation for Young Scientist (No. 02J20102-13)     

Pure bending of simply supported circular plate of transversely isotropic functionally graded material

INTRODUCTION In recent years, functionally graded materials (FGMs) have attracted more and more attention. Due to their continuously varying material properties in space on the macroscopic scale, FGMs, therefore, are usually superior to conventional fiber-matrix materi-als in mechanical behavior, especially for perform-ance under thermal loading. Now FGMs have been widely used in various fields including electronics, chemistry, optics, biomedicine, etc. Heretofore, volumes of literatu…     

Ultimate Bearing Capacity of Hollow Spherical Joints Welded with Circular Pipes under Eccentric Loads

The National Swimming Center built for the 2008Beijing Olympic Games applies the polyhedron spatialframe structure, which is based on the foam physicstheory[1]. Its simple geometry is a square box of 170m×170 m×29 m. It can hold 17 000 people, theroof o…     

均布载荷作用下厚矩形板的弯曲

推广应用功的互等定理法(RTM)于求解基于Reissner理论的厚矩形板的弯曲问题，给出了二对边简支另两边固定厚矩形板在均布载荷作用下弯曲的精确解析解，并分析了解的数值结果．     

利用影响线计算力偶作用时梁的内力和反力

将力偶分解为等值、反向、平行的两个力,当荷载(集中荷载、分布荷载和力偶)位置已知时,利用影响线计算梁的内力和反力,并与截面法计算结果作一比较。     

Dynamical stability of finite anisotropic panels with elliptical cutouts and cracks

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固支圆板在线性荷载作用下的极限解

运用双剪统一屈服准则,对线性荷载的两种不同分布形式作用下的固支圆板进行了弹塑性分析,分别得出了相应的统一解形式。选择不同的参数。利用本文的解可以得到一系列不同屈服准则下的极限荷载和极限荷载随不同屈服准则的变化曲线。所给出的统一解适用于各种拉压强度相同的材料。文献中已有的Mises解是本文解答的逼近。计算结果表明,应用双剪统一屈服准则可以得出更符合材料性质的极限荷载,可以更好地发挥材料的强度潜力,在工程应用中取得显著的经济效益。     

Analytical solution for fixed-end beam subjected to uniform load

A bi-harmonic stress function is constructed in this work. Ariy stress function methodology is used to obtain a set of analytical solutions for both ends fixed beams subjected to uniform load. The treatment for fixed-end boundary conditions is the same as that presented by Timoshenko and Goodier （1970）. The solutions for propped cantilever beams and cantilever beams are also presented. All of the analytical plane-stress solutions can be obtained for a uniformly loaded isotropic beam with rectangular cross section under different types of classical boundary conditions.     

Science Letters:Analytical solution for fixed-end beam subjected to uniform load

INTRODUCTION The plane stress problem of beams is very clas-sical in elasticity theory and is encountered frequently in practical cases. Timoshenko and Goodier (1970) investigated isotropic beams for different cases, such as tension, shearing, pure bending, bending of a can-tilever by transverse load at the end, bending of a simply supported beam by uniform load and other cases of continuously loaded beams. Lekhnitskii (1968) studied the anisotropic beams problem including tension, shear…     

In-plane creep buckling of concrete-filled steel tubular arches

The creep-induced deformation of the arch rib of concrete-filled steel tubular （CFST） arches under a sustained load can increase the bending moment, which may lead to earlier stability failure called creep buckling. To investigate the influences of concrete creep on the buckling strength of arches, a theoretical analysis for the creep buckling of CFST circular arches under distributed radial load is performed. The simplified Arutyunyan-Maslov （AM） creep law is used to model the creep behavior of concrete core, and the creep integral operator is introduced. The analytical solutions of the time-dependent buckling strength under the sustained load are achieved and compared with the existing formula based on the age-adjusted effective modulus method （AEMM）. Then the solutions are used to determine the influences of the steel ratio and the first loading age on the creep buckling of CFST arches. The results show that the analytical solutions are of good accuracy and applicability. For CFST arches, the steel ratio and the first loading age have significant influences on creep buckling. An approximate log-linear relationship between the decreased degrees of the creep buckling strength and the first loading age is found. For the commonly used parameters, the maximum loss of the buckling strength induced bv concrete creen is close to 40%     

Theoretical solution of a spherically isotropic hollowsphere for dynamic thermoelastic problems

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