Analytic elasticity solution of bi-modulus beams under combined loads

A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤ 5. The error also varies with the distributed load patterns.

General Analytical Shakedown Analysis of a Structure Subjected to Combined Loading with Constant and Cyclic Loads

The shakedown behavior of structures subjected to a combined loading of constant and cyclic loads has been well researched.For some specified problems,shakedown limit loads have been obtained.However,the general effect of combined loading on the structural shakedown has not yet been presented.The general analytic solution of the elastic shakedown limit load is thus derived for a structure subjected to combined loading.Polizzotto's extended static shakedown theorem for combined loading is applied.The stress field in equilibrium with the external constant load required in Polizzotto's extended theorem is constructed by subtracting the reference elastic stress field of the peak cyclic load from the elastic-plastic stress field of the combined constant load and peak cyclic load.The shakedown condition of the stress field is then derived according to the extended theorem.Through the analytical analysis of the shakedown condition,the structural shakedown behavior under combined loading is investigated.A general solution of the shakedown limit load is then derived,and the effects of the combined loading on the shakedown behavior are proposed.The obtained general analytical result is applied to a hollow tension specimen under constant tension and alternating torsion and a plate with a central hole under constant and cyclic tension.The results are consistent with the solutions reported in the literature.

非均匀地应力场中套管载荷的理论解

利用弹性力学理论推导出了非均匀地应力条件下套管-地层系统的位移场、应力场和套管载荷的解析表达式。将非均匀地应力分解为均匀地应力和偏差地应力两部分,并用弹性力学方法分别对其进行求解,得出理论解,最后将两部分叠加得到非均匀地应力条件下的套管-地层系统的位移场、应力场和套管载荷。应用实例表明,套管径向压力载荷图形的长轴指向地应力场的最小主压应力方向。

水平受荷桩的耦合算法

目前,计算水平受荷桩基时较为流行的是p—y 曲线法和Poulos 弹性理论法。本文在p—y 曲线法和Poulos 弹性理论法的基础上,提出一种能够考虑两者优点的耦合算法。根据p—y 曲线法分析得出相对于不同土体应力状态的弹性模量,利用分析得出的弹性模量,采用Poulos 弹性理论法考虑桩土之间的相互作用。实例分析表明,提出的耦合算法能够较为有效地分析水平受荷桩基。

流变地层地应力场中套管载荷的理论解

利用求解线性粘弹性问题的弹性粘弹性对应性原理,利用已有的弹性解,求得了考虑地层符合Kelvin流变规律的情况下,地应力场中套管载荷的理论解,并给出了松弛时间的解析表达式。研究表明,流变地层地应力场中套管载荷随时间变化,存在一临界时间,使得套管载荷有最值,当时间足够长时,粘弹性解与相应的弹性解一致。用套管弹性解定义的套管地应力载荷,稍低于流变地层中套管所受最大压力。因此在设计时,或者将弹性计算载荷适当增大,或者将安全系数适当增大,以保证套管安全。

非均匀地应力下套管的抗外挤强度理论解

从非均匀载荷产生的原因出发,结合钻井工程的实际情况,讨论了固井后套管边界的受力情况,并建立了套管在非均匀载荷作用下的力学模型,采用弹性力学逆解法求得了该问题的解析解。在此基础上,根据套管的应力分布规律提出了非均匀外载等效成均匀外载的方法。并结合含磨损、残余应力等缺陷套管在均匀外压下的抗挤强度,提出了套管在非均匀载荷下的抗挤强度计算方法。