Wolfram Language

Impresión en 3D

Detección de problemas de diseño antes de la impresión en 3D

Utilice las capacidades numéricas de solución de ecuaciones diferenciales en Wolfram Language para detectar problemas con sus diseños antes de emprender el gasto de la impresión en 3D.

Realice un análisis de estrés y modele la deformación de un cigüeñal montado.

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muestre la entrada completa de Wolfram Language
In[2]:=
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(* load the finite element package and create a finite element mesh *) \ Needs["NDSolve`FEM`"] crankshaft = ToElementMesh[DiscretizeGraphics[crankshaft], "MeshOrder" -> 1]; (* Specify the 3D stress formulation *) stressOperator[ Y_, \[Nu]_] := {Inactive[ Div][({{0, 0, -((Y \[Nu])/((1 - 2 \[Nu]) (1 + \[Nu])))}, {0, 0, 0}, {-(Y/(2 (1 + \[Nu]))), 0, 0}}.Inactive[Grad][ w[x, y, z], {x, y, z}]), {x, y, z}] + Inactive[ Div][({{0, -((Y \[Nu])/((1 - 2 \[Nu]) (1 + \[Nu]))), 0}, {-(Y/(2 (1 + \[Nu]))), 0, 0}, {0, 0, 0}}.Inactive[Grad][ v[x, y, z], {x, y, z}]), {x, y, z}] + Inactive[ Div][({{-((Y (1 - \[Nu]))/((1 - 2 \[Nu]) (1 + \[Nu]))), 0, 0}, {0, -(Y/(2 (1 + \[Nu]))), 0}, {0, 0, -(Y/(2 (1 + \[Nu])))}}.Inactive[Grad][ u[x, y, z], {x, y, z}]), {x, y, z}], Inactive[ Div][({{0, 0, 0}, {0, 0, -((Y \[Nu])/((1 - 2 \[Nu]) (1 + \[Nu])))}, {0, -(Y/( 2 (1 + \[Nu]))), 0}}.Inactive[Grad][ w[x, y, z], {x, y, z}]), {x, y, z}] + Inactive[ Div][({{0, -(Y/(2 (1 + \[Nu]))), 0}, {-((Y \[Nu])/((1 - 2 \[Nu]) (1 + \[Nu]))), 0, 0}, {0, 0, 0}}.Inactive[Grad][u[x, y, z], {x, y, z}]), {x, y, z}] + Inactive[ Div][({{-(Y/(2 (1 + \[Nu]))), 0, 0}, {0, -((Y (1 - \[Nu]))/((1 - 2 \[Nu]) (1 + \[Nu]))), 0}, {0, 0, -(Y/(2 (1 + \[Nu])))}}.Inactive[Grad][ v[x, y, z], {x, y, z}]), {x, y, z}], Inactive[ Div][({{0, 0, 0}, {0, 0, -(Y/(2 (1 + \[Nu])))}, {0, -(( Y \[Nu])/((1 - 2 \[Nu]) (1 + \[Nu]))), 0}}.Inactive[Grad][ v[x, y, z], {x, y, z}]), {x, y, z}] + Inactive[ Div][({{0, 0, -(Y/(2 (1 + \[Nu])))}, {0, 0, 0}, {-((Y \[Nu])/((1 - 2 \[Nu]) (1 + \[Nu]))), 0, 0}}.Inactive[Grad][u[x, y, z], {x, y, z}]), {x, y, z}] + Inactive[ Div][({{-(Y/(2 (1 + \[Nu]))), 0, 0}, {0, -(Y/(2 (1 + \[Nu]))), 0}, {0, 0, -(( Y (1 - \[Nu]))/((1 - 2 \[Nu]) (1 + \[Nu])))}}.Inactive[ Grad][w[x, y, z], {x, y, z}]), {x, y, z}]}; (* Specify constraints such that the boundary of the crankshaft is \ held fixed at these positions *) Subscript[\[CapitalGamma], D] = {DirichletCondition[{u[x, y, z] == 0., v[x, y, z] == 0., w[x, y, z] == 0.}, {y <= 0.1, y >= 890}]}; (* Specify a boundary load pushing in the negative z\[Hyphen]axis *) Subscript[\[CapitalGamma], L] = NeumannValue[-10000., ((217 <= y <= 256) && (40 <= z <= 103)) || ((584 <= y <= 622) && (40 <= z <= 103))]; (* visualization *) showStress[{uif_, vif_, wif_}] := Show[ ToBoundaryMesh[crankshaft][ "Wireframe"[ "MeshElementStyle" -> {Directive[EdgeForm[], FaceForm[Gray]]}]], ElementMeshDeformation[crankshaft, {uif, vif, wif}, "ScalingFactor" -> 100][ "Wireframe"[AspectRatio -> Automatic, "MeshElementStyle" -> Directive[EdgeForm[], FaceForm[Red]]]], ImageSize -> 300, ViewPoint -> {-2, -2, 0} ]

Encuentre las propiedades del material de acero.

In[3]:=
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WolframAlpha["young modulus of steel in Pa", "WolframResult"]
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WolframAlpha["Poisson ratio of steel", "WolframResult"]
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Resuelva y visualice la deformación.

In[5]:=
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NDSolveValue[{stressOperator[2.05*10^11, 0.29] == {0, 0, Subscript[\[CapitalGamma], L]}, Subscript[\[CapitalGamma], D]}, {u, v, w}, {x, y, z} \[Element] crankshaft] // showStress
Out[5]=

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