A Perturbation Result for Dynamical Contact Problems

This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover,it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method.We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions.For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law,we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space.This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries.Furthermore,we present perturbation results for two well-established approximations of the classical Signorini condition:The Signorini condition formulated in velocities and the model of normal compliance,both satisfying even a sharper version of our stability condition.

基于纽玛克法的变截面波形钢腹板组合箱梁畸变效应分析

为研究变截面波形钢腹板组合箱梁(CBGCSWs)在偏心荷载作用下的畸变效应,忽略波形钢腹板的纵向抗弯刚度,通过建立其微段单元平面内、外力系平衡方程,推导了以畸变角为未知量的畸变微分方程,并采用基于共轭梁理论的纽玛克法进行求解,由此建立了偏心荷载作用下变截面CBGCSWs畸变正应力计算理论。以某大跨变截面CBGCSWs桥为工程背景,运用该理论获得了4种不同工况下组合箱梁角点处畸变正应力理论解,并采用空间有限元方法进行了验证,数值解与理论解吻合良好,表明推导的变截面CBGCSWs畸变计算理论正确且精度足够,可供工程参考。在此基础上,比较了变截面CBGCSWs与对应PC箱梁的抗畸变能力,并探讨了横隔板间距、高跨比、宽跨比及钢腹板形状等因素对变截面CBGCSWs畸变正应力的影响规律。结果表明:用波形钢腹板替代混凝土腹板会较大程度削弱箱梁的抗畸变能力,应当引起足够重视;横隔板间距及宽跨比等参数对畸变正应力影响较大,而高跨比及钢腹板形状等则影响很小。