Optimization of a Symmetric Tapered Beam

This tool computes the optimal dimensions L₁, L₂, h, t_min , t_max for a square‐section symmetric tapered beam so as to minimize its total length L₁+h+L₂ subject to given stiffness deflection and stress limits. Enter material properties (Young's modulus e, shear modulus g), target stress c, stiffness K₀, deflection d, and number of beams; it then finds the load P, the maximum stress location  r+rL₁, and outputs the optimal half‐length L₁and thickness bounds t_min/t_max.

In the optimal design, the straight middle segment h is zero, this is L₂ = L₁ and the maximum stress happens at L₁+ r L₁. All cross‐sections remain perfect squares.

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Results

The value for P is: 30.000000

The value for r is: 0.615026

The value for L₁=L₂ is: 0.895426

The value for t_min is: 0.101265

The value for t_max is: 0.183591

The minimum value for L₁ + L₂ is: 1.790852