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在球面坐标系中计算应变和应力

在球面坐标系中计算应变和应力

在弹性介质理论中，材料的应力是4阶刚度张量（材料的一种属性）和2阶应变（其形变的一种属性）的缩并. 应变为形变场的对称化梯度.

    
Wolfram Language code: u[r_, θ_, φ_] := {Subscript[u, "r"][r, θ, φ], Subscript[u, "θ"][r, θ, φ], Subscript[u, "φ"][r, θ, φ]}
Wolfram Language code: strain = Symmetrize[Grad[u[r, θ, φ], {r, θ, φ}, "Spherical"]]//Simplify; strain//SymmetrizedArrayRules//Most
Wolfram Language code: stiff = SymmetrizedArray[pos_ :> Subscript[c, StringJoin[{"r", "θ", "φ"}[[pos ]]]], {3, 3, 3, 3}, {Symmetric[{1, 2}], {{3, 4, 1, 2}, 1}}] stress = TensorContract[stiffstrain, {{3, 5}, {4, 6}}]//Simplify; stress//SymmetrizedArrayRules//Most