Wolfram Language

Impression 3D

Détectez des problèmes de conception avant l'impression 3D

Utilisez des capacités numériques de solution d'équations différentielles en Wolfram Language pour détecter des problèmes avec vos dessins avant d'entreprendre la charge de l'impression 3D.

Effectuez l'analyse des contraintes et modélisez la déformation d'un vilebrequin monté.

In[1]:=
Click for copyable input
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Montrer l'entrée complète de Wolfram Language
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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} ]

Trouvez les propriétés des matériaux en acier.

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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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Résolvez et visualisez la déformation.

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
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Exemples connexes

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