Energy balance 能量平衡

GLSTAT(参见 *database_glstat)文件中报告的总能量是下面几种能量的和：

1. 内能 internal energy
2. 动能 kinetic energy
3. 接触（滑移）能 contact(sliding) energy
4. 沙漏能 houglass energy
5. 系统阻尼能 system Damping energy
6. 刚性墙能量 rigidwall energy

“Spring and damper energy”reported in the glstat file is the sum of internal energy of discrete elements, seatbelt elements, and energy associated with joint stiffnesses (*constrained_joint_stiffness…….).“Internal Energy”includes“Spring and damper energy”as well as internal energy of all other element types. Thus“Spring and damper energy”is a subset of“Internal energy”。

GLSTAT 中报告的弹簧阻尼能”Spring and damper energy”是离散单元（discrete elements)、安全带单元 (seatbelt elements) 内能及和铰链刚度相关的内能 (*constrained_joint_stiffness……) 之和。而内能 ”Internal Energy” 包含弹簧阻尼能 ”Spring and damper energy” 和所有其它单元的内能。 因此弹簧阻尼能 ”Spring and damper energy” 是内能 ”Internal energy” 的子集。

The“joint internal energy”written to glstat by SMP 5434a is independent of the constrained_joint_stiffness. It would appear to be associated with the penalty stiffness of *constrained_joint_revolute (_spherical, etc). This was a missing energy term prior to SMP rev. 5434a. It is still a missing energy term in MPP rev. 5434a. It does NOT appear when a Lagrange Multiplier formulation is used.

由 SMP 5434a 版输出到 glstat 文件中的铰链内能”joint internal energy”跟 *constrained_joing_stiffness 不相关。它似乎与 *constrained_joint_revolute(_spherical,etc)的罚值刚度相关连。这是 SMP 5434a 之前版本都存在的缺失的能量项，对 MPP 5434a 也一样。这种现象在用拉格朗日乘子（Lagrange Multiplier)方程时不会出现。

The energy associated with *constrained_joint_stiffness appears in the jntforc file and is included in glstat in“spring and damper energy”and“internal energy”。 Recall that“spring and damper energy”， whether from joint stiffness or from discrete elements, is always included in“internal energy”。

与 *constrained_joint_stiffness 相关的能量出现在 jntforc 文件中，也包含在 glstat 文件中的弹簧和阻尼能和内能中。回想弹簧阻尼能”spring and damper energy”，不管是从铰链刚度还是从离散单元而来，总是包含在内能里面。

在 MATSUM 文件中能量值是按一个 part 一个 part 的输出的（参见 *database_matsum)。

Hourglass energy is computed and written only if HGEN is set to 2 in *control_energy. Likewise, rigidwall energy and Damping energy are computed and written only if RWEN and RYLEN, respectively, are set to 2. Stiffness Damping energy is lumped into internal energy. Mass Damping energy appears as a separate line item“system Damping energy”。

沙漏能 Hourglass energy 仅当在卡片 *control_energy 中设置 HGEN 项为 2 时才计算和输出。同样，刚性墙能和阻尼能仅当上面的卡片中 RWEN 和 RYLEN 分别设置为 2 时才会计算和输出。刚性阻尼能集中到内能里面。质量阻尼能以单独的行”system Damping energy”出现。由于壳的体积粘性（bulk viscosity)而产生的能量耗散（energy dissipated)在版本 970.4748 之前是不计算的。在后续子版本中，设置 TYPE=- 2 来在能量平衡中包含它。

最理想的情况下能量平衡：

总能量 total energy = 初始总能量 + 外力功 external work

换句话说，如果能量比率 energy ratio(指的是 glstat 中的 total energy/initial energy，实际上是 total energy/(initial energy + external work)) 等于 1.0。注意，质量缩放而增加质量可能会导致能量比率增加。

Note that added mass may cause the energy ratio to rise. (See ~/test/erode/taylor.mat3.noerode.mscale.k)
The History > Global energies do not include the contributions of eroded elements whereas the GLSTAT energies do include those contributions. Note that these eroded contributions can be plotted as“Eroded Kinetic Energy”and“Eroded Internal Energy”via ASCII > glstat. Eroded energy is the energy associated with deleted elements (internal energy) and deleted nodes (kinetic energy). Typically, the“energy ratio w/o eroded energy”would be equal to 1 if no elements have been deleted or less than one if elements have been deleted.  The deleted elements should have no bearing on the“total energy / initial energy”ratio.  Overall energy ratio growth would be attributable to some other event, e.g., added mass. Restated, when an element erodes, the internal energy and kinetic energy in glstat do not reflect the energy loss. Instead the energy losses are recorded as“eroded internal energy”and“eroded kinetic energy”in glstat. If you subtract“eroded internal energy”from“internal energy”， you have the internal energy of elements which remain in the simulation. Likewise for kinetic energy. The matsum file’s internal energy and kinetic energy include only contributions from the remaining (noneroded) elements.

注意在 LSprepost 的 History>Global energies 中不包含删掉的单元（eroded elements)的能量贡献，然而 GLSTAT 文件中的能量包含了它们。注意它们的贡献可以通过 ASCII>glstat 中的”Eroded Kinetic Energy”&“Eroded Internal Energy”来绘制。侵蚀能量（Eroded energy)是与删掉的单元相关的内能和删掉的节点相关的动能。典型来说，如果没有单元删掉”energy ratio w/o eroded energy”等于 1，如果有单元被删掉则小于 1。删掉的单元与”total energy/initial energy”比率没有关系。总能量比率增加要归于其它原因，比如增加质量。重述一下，将一个单元删掉时，文件 glstat 中的内能和动能不会反映能量的丢失。取而代之的是能量的丢失记录在 glstat 文件的”eroded internal energy”&“eroded kinetic energy”中。如果用内能减去”eroded internal energy”将得到分析中还存在的单元的内能。对动能也一样。