Elliptic integral solutions of spatial elastica of a thin straight rod bent under concentrated terminal forces

In this article, we solve in closed form a system of nonlinear differential equations modelling the elastica in space of a thin, flexible, straight rod, loaded by a constant thrust at its free end. Common linearizations of strength of materials are of course not applicable any way, because we analyze great deformations, even if not so large to go off the linear elasticity range. By passing to cylindrical coordinates ρ, θ, z, we earn a more tractable differential system evaluating ρ as elliptic function of polar anomaly θ and also providing z through elliptic integrals of I and III kind. Deformed rod’s centerline is then completely described under both tensile or compressive load. Finally, the planar case comes out as a degeneracy, where the Bernoulli lemniscatic integral appears.     

Evaluation of cyclic plasticity models in ratcheting simulation of straight pipes under cyclic bending and steady internal pressure

This paper evaluates seven cyclic plasticity models for structural ratcheting response simulations. The models evaluated are bilinear (Prager), multilinear (Besseling), Chaboche, Ohno–Wang, Abdel Karim–Ohno, modified Chaboche (Bari and Hassan) and modified Ohno–Wang (Chen and Jiao). The first three models are already available in the ANSYS finite element package, whereas the last four were implemented into ANSYS for this study. Experimental responses of straight steel pipes under cyclic bending with symmetric end rotation history and steady internal pressure were recorded for the model evaluation study. It is demonstrated that when the model parameters are determined from the material response data, none of the models evaluated perform satisfactorily in simulating the straight pipe diameter change and circumferential strain ratcheting responses. A detailed parameter sensitivity study with the modified Chaboche model was conducted to identify the parameters that influence the ratcheting simulations and to determine the ranges of the parameter values over which a genetic algorithm can search for refinement of these values. The refined parameter values improved the simulations of straight pipe ratcheting responses, but the simulations still are not acceptable. Further, improvement in cyclic plasticity modeling and incorporation of structural features, like residual stresses and anisotropy of materials in the analysis will be essential for advancement of low-cycle fatigue response simulations of structures.     

The bending of set squares with one free oblique edge under a concentrated load

I-Introduction-Itisveryimportanttoresearchonthebendingofelasticthinplateinpractice.Alotofworkaboutthisproblemhavebeendonebythescholarsandexpertsofmanycountriesintheworld.However.therearefewpeoplewhostudied-thebendingofsetsquareundervarioussupportsandloads…     

Problems of collinear cracks between bonded dissimilar materials under antiplane concentrated forces

In this paper problems of cullinear cracks between bonded dissimilar materials underantiplane concentrated forces are dealt with.General solutions of the problems areformulated by applying extended Schwarz principle integrated with the analysis of thesingularity of complex stress functions.Closed-form solutions of several typical problemsare obtained and the stress intensity factors are given.These solutions include a series oforiginal results and some results of previous researches.It is found that under symmetricalloads the solutions for the dissimilar materials are the same as those for the homogeneousmaterials.     

Bending of rectangular plate with each edges arbitrary a point supported under a concentrated load

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｅｎｇｉｎｅｅｒｉｎｇｔｅｃｈｎｏｌｏｇｙ,ｔｈｅｂｅｎｄｉｎｇｐｒｏｂｌｅｍｏｆｅｌａｓｔｉｃｔｈｉｎｐｌａｔｅｈａｓｉｍｐｏｒｔａｎｔｐｒａｃｔｉｃａｌｓｉｇｎｉｆｉｃａｎｃｅ,ａｎｄａｌｏｔｏｆｒｅｓｕｌｔｓｈａｖｅｂｅｅｎｏｂｔａｉｎｅｄ.Ｂｅｃａｕｓｅｔｈｅｐｒｏｂｌｅｍｓｏｆｅａｃｈｅｄｇｅｓｐｏｉｎｔｓｕｐｐｏｒｔｅｄａｒｅｃｏｍｐｌｅｘｅｒ,ｔｈｅｒｅａｒｅｆｅｗｒｅｓｕｌｔｓｏｆｔｈｅｐｒｏｂｌｅｍｓ.Ｉｎｔｈｅｐａｐｅｒ[1],ｔｈｅｍｅｔｈｏｄｏｆｓｕｐ…     

局部荷载作用下有梁矩形板的弹性分析

写出了任意局部荷载作用下各种不同边界条件矩形板的解的表达式．通过梁与板的边界协调分析，求出不同荷载作用下的有梁矩形板解析解，并通过改变其中参数EI与GIt的数值，可以得出局部荷载作用下各种不同边界条件下矩形板的解．     

Deformation of flexible noncircular cylindrical shells under concurrent loads of two types

The paper presents an exact analytic solution to a nonlinear boundary-value problem for a long noncircular cylindrical shell with variable cross-sectional curvature under two concurrent loads: a surface force and bending moments. The behavior of the shell under these loads is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 58–65, July 2007.