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2025-04-22

VE0035 | Mixed Dimensional Coupling

请证明，不同量纲单元的耦合不会影响结果。选择一个矩形截面的悬臂梁，对另一端施加 F_x和 F_z的荷载。忽略其自重并假设只有很小的变形，计算悬臂梁的最大轴向挠度 u_x 、横向挠度 u_z和总挠度 u。

Mixed Dimensional Coupling

Deflection of the cantilever with a rectangular cross-section in the axial (X) direction can be calculated according to the following formula:

u_{x} = \frac{F_{x} L}{E b h} = 5.000 m m

轴向挠度

Deflection in the transversal direction (Z), including shear effect, can be calculated according to the following formula:

u_{z} = \frac{4 F_{z} L^{3}}{E b h^{3}} + β \frac{2 F_{z} L}{E b h} = 20.001 mm

β	与截面形状有关的参数

横向挠度

对于矩形截面，参数 β 为1.2。 Finally, the total deflection of the cantilever can be calculated.

u = \sqrt{u_{x}^{2} + u_{z}^{2}} = 20.617 m m

悬臂梁的总挠度

410x

11x

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