Engineering Encyclopedia · ToolingWorkbench v1 — Geometry Core

Engineering WorkbenchSketch · Snap · Extrude · Orbit · Annotate

Sketch
Snap mm

Sketch Plane mm · grid 10

Pick a tool and draw a closed profile. Rectangle: drag. Circle: drag from centre. Polygon: click vertices, click the first to close.
Extrude height mm Material

Model orbit: drag · zoom: wheel / ±

Place

Boundary conditions & features

  • None placed. Pick a Place tool, then tap a face of the solid.
What is exact, what is not. Geometry and the mass / volume / area / surface readouts are computed exactly from your profile and extrude height. Boundary conditions you place are recorded with their coordinates and face normal — they are inputs for analysis, not solved results. Running real stress, heat, or flow fields on this solid needs a mesh generator and a numerical solver, which is the next, heavier rung. Exports below are real: DXF profile, OBJ solid, and a JSON of the full setup.

Analysis · Cantilever Beam Euler–Bernoulli · closed-form · verifiable

Cross-section — draw a profile, then Solve —
Length L mm Tip load P N
Load dir.
Modulus & yield come from the Material selector above. Fix / Force markers mark the built-in end and the loaded tip.
statusdraw → extrude → Solve
Assumptions & validity. Prismatic beam, isotropic linear-elastic material, small deflection (δ ≪ L), transverse point load at the free tip, plane sections remain plane, no shear deformation. Beam theory is accurate only for slender beams (length ≳ 10 × section depth) and stresses below yield — both are checked and flagged below. The moment of area is computed exactly from your sketched profile (true polygon / circle formula), so these numbers can be checked by hand: a rectangle b×h gives I = b·h³/12 and σ = 6PL/(b·h²).

Analysis · 1D Transient Heat Conduction Fourier series · closed-form · verifiable

Bar length L mm Material from selector ↑
Initial T_i °C End temp T_s °C
Time
t = 0 s
statusset temps → Solve
Assumptions & validity. One-dimensional conduction in a homogeneous bar of length L, both ends held at T_s, uniform initial T_i, constant properties, no internal heat generation, insulated sides. Exact Fourier series θ(x,t)=Σ₍odd₎ (4/nπ)·sin(nπx/L)·e^(−(nπ/L)²αt), with α = k/(ρ·c_p). Check by hand: the centre cools as θ ≈ (4/π)·e^(−t/τ), τ = L²/(π²α); by Fourier number Fo = αt/L² ≈ 0.2 the centre has responded substantially.

Analysis · Parallel-Plate Capacitor Electrostatics · closed-form · verifiable

Plate area A cm² Gap d mm
Voltage V V Dielectric κ
statusset values → Solve
Assumptions & validity. Ideal parallel plates, uniform field, fringing at the edges neglected (valid when plate size ≫ gap), linear homogeneous dielectric, electrostatic (no time variation). Closed form: E = V/d, C = κε₀A/d, energy U = ½CV². Check by hand: 100 V across a 1 mm gap is E = 100 kV/m exactly; ε₀ = 8.854×10⁻¹² F/m.