1) minimum potential energy theorem
最小势能定理
2) minimal potential energy principle
最小势能原理
1.
Since,the total potential energy of woven fabrics,is in spline function with the yarn shape curve,the minimal potential energy principle is satisfied when the system is stable.
首先对被施加外部荷载的织物建立数学模型,由于相应的机织织物结构的总势能U是关于纱线形状曲线的泛函,当系统稳定时满足最小势能原理,通过求泛函极值,获得机织织物结构中纱线路径的较为真实的形状曲线,从而为描述机织织物结构几何模型和力学模型提供了相应的理论途径。
3) principle of minimum potential energy
最小势能原理
1.
Application of principle of minimum potential energy to spatial deformation analysis for deep foundation pit with anchored pile supporting;
基于最小势能原理的桩锚支护结构空间变形分析
2.
Research on bending of the cantilever based on the principle of minimum potential energy
基于最小势能原理的悬臂梁弯曲研究
3.
Based on the differential equation for curvature of beams,the theory of finite element and the principle of minimum potential energy,a method for beams on Winkler foundation under complex conditions was deduced with compatibility conditions of displacement,angular rotation,moment and shear of adjacent beam elements.
基于梁的弯曲微分方程、有限元理论和最小势能原理(虚功原理),利用梁单元间的位移、转角、弯矩和剪力协调条件,地基梁的整体平衡条件,给出了复杂条件下Winkler地基梁的一种计算方法。
4) minimum potential energy
最小势能原理
1.
First we suppose a deflection expression on principle of minimum potential energy for an opening elastic rectangular thin plate loaded with critical force, which can meet the side conditions of displacement or force.
从弹性带孔矩形薄板稳定最小势能原理出发,首先设定临界力作用下的挠度表达式,使之满足箱形井塔薄板的位移或力的边界条件,然后依据整个矩形的板面积除去孔口部分的面积进行积分推演,导出最小势能原理在不同边界约束下开孔矩形薄板临界力计算公式。
2.
With the principle of the minimum potential energy,an analytical solution for the lateral critical bucking lord of tied-arch bridges is studied.
利用最小势能原理推导了肋拱桥结构在外荷载作用下侧倾稳定临界力的近似解析解。
3.
In this paper, the bending problem of unbonded contact of beams on tensionless winkler foundations is investigated by sine series and principle of minimum potential energy.
利用正弦级数和最小势能原理,解答了无拉力Winkler地基上梁的脱离问题。
5) the principle of minimum potential energy
最小势能原理
1.
Based on the engineering background of Zhongguancun Culture Building of a 30m×70m planar cable-net, the vibration equation of a prestressed rectangular cable-net is deduced by the principle of minimum potential energy considering the influence of geometric nonlinearity of large deformation, and the solution to the equation is given.
以中关村文化商厦30m×70m平面索网为工程背景,考虑矩形索网结构大变形产生的几何非线性的影响,用最小势能原理推导了非线性振动的微分方程并给出了解法;研究了线性振动频率、大振幅振动频率和大变形后小振幅的振动频率计算方法;结合实例对3个振动频率进行了计算分析。
2.
A mechanical model of coal pillar stability and of rheological properties of the back fill was established using the principle of minimum potential energy.
将充填体视为黏弹塑性介质,利用最小势能原理,在分析充填体与顶板的相互关系以及充填体受力状况后,建立了考虑顶板刚度及充填体软化与流变特性的分析模型。
6) minimum potential energy principle
最小势能原理
1.
The governing differential equations and boundary conditions considering multi-factor of thin walled curved box girders are established by minimum potential energy principle to analyze the shear lag effect,which set the foundation of theoretical analysis of shear lag effect in thin walled box girders by multi-factor.
利用最小势能原理建立了考虑多因素的分析薄壁曲线箱梁剪滞效应的控制微分方程及其边界条件,为考虑多因素薄壁箱梁剪滞效应建立了理论分析基础。
2.
The governing differential equations and boundary conditions considering multi-parameters and shear deformation of thin walled box girders are established by minimum potential energy principle to analyze the shear lag effect, which set the foundation of theoretical analysis of shear lag effect in thin walled box girders by multi-parameter.
利用最小势能原理建立了考虑多参数及剪切变形的分析薄壁箱梁剪滞效应的控制微分方程及其边界条件 ,为考虑多参数薄壁箱梁剪滞效应建立了理论分析基础 。
3.
The minor deflection of sheet using the minimum potential energy principle was carried out elastic analysis, the approximate calculating methods of sheet was derived.
利用最小势能原理对小挠度薄板进行弹性分析,并给出薄板的近似计算的方法,同时,还具体地计算了受均布载荷作用的板的挠度。
补充资料：弹性力学最小势能原理
弹性力学的能量原理之一，它可表述为：整个弹性系统在平衡状态下所具有的势能，恒小于其他可能位移状态下的势能。其中可能位移是指满足变形连续条件和位移边界条件的位移，用来表示。整个弹性系统的势能∏的表示式为：
式中左侧为真实位移ui对应的势能；右侧第一项为弹性体中的应变能,u(εij)为应变能密度,εij为应变分量，Ω为物体所占空间；第二项为体积力构成的势能，fi为体积力分量；第三项为边界外力构成的势能，圴i为给定的面力分量,B2为给定外力的边界面，dB是B2上的面积微元；式中重复下标表示约定求和。
最?∈颇茉砜尚次?
∏(ui)≤∏()，式中的等号只有在可能位移就是真实位移的情况下才成立。最小势能原理实质上等价于弹性体的平衡条件。它可作为弹性力学直接解法和有限元计算（见有限元法）的重要基础。
式中左侧为真实位移ui对应的势能；右侧第一项为弹性体中的应变能,u(εij)为应变能密度,εij为应变分量，Ω为物体所占空间；第二项为体积力构成的势能，fi为体积力分量；第三项为边界外力构成的势能，圴i为给定的面力分量,B2为给定外力的边界面，dB是B2上的面积微元；式中重复下标表示约定求和。
最?∈颇茉砜尚次?
∏(ui)≤∏()，式中的等号只有在可能位移就是真实位移的情况下才成立。最小势能原理实质上等价于弹性体的平衡条件。它可作为弹性力学直接解法和有限元计算（见有限元法）的重要基础。
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