lemma A.685 The Gaussian-curvature term is a null Lagrangian

open in the book · appendices/A-long-proofs.tex:33332 · p. 3126

Rests on

depends_on proposition A.684 The plate energy ¶
- depends_on definition 30.63 Flexural rigidity ¶
  - depends_on proposition 30.33 Conversion among the moduli ¶
    - depends_on definition 30.31 The engineering moduli ¶
      - depends_on definition 30.20 Pressure and deviatoric stress ¶
      - depends_on equation 30.21 eq:elast-hooke-isotropic ¶
    - depends_on phenomenon 30.32 Poisson contraction ¶
      - depends_on phenomenon 30.28 Hooke's law ¶
      - depends_on proposition 30.30 Stability bounds ¶
      - proves proof ch:13-continuum-elasticity@proof-14 ¶
    - proves proof ch:13-continuum-elasticity@proof-15 ¶
  - depends_on proposition 30.51 Moment and curvature ¶
    - depends_on definition 30.31 The engineering moduli ¶ ↺
    - depends_on equation 30.21 eq:elast-hooke-isotropic ¶ ↺
    - proves proof ch:13-continuum-elasticity@proof-27 ¶
- depends_on lemma A.681 Strains under the Kirchhoff hypothesis ¶
  - depends_on definition A.680 Kirchhoff kinematics ¶
    - depends_on definition 30.6 Linear strain and infinitesimal rotation ¶
      - depends_on definition 13.91 Symmetric and antisymmetric parts ¶
      - depends_on equation 30.2 eq:elast-displacement ¶
    - depends_on proposition 30.51 Moment and curvature ¶ ↺
  - depends_on definition 30.6 Linear strain and infinitesimal rotation ¶ ↺
  - proves proof app:A-long-proofs@proof-404 ¶
- depends_on proposition A.682 The plane-stress law ¶
  - depends_on definition 30.63 Flexural rigidity ¶ ↺
  - depends_on equation 30.21 eq:elast-hooke-isotropic ¶ ↺
  - depends_on proposition 30.33 Conversion among the moduli ¶ ↺
  - proves proof app:A-long-proofs@proof-405 ¶
- proves proof app:A-long-proofs@proof-406 ¶
proves proof app:A-long-proofs@proof-407 ¶

Supports

depends_on remark A.686 Why the operator comes out as $\nabla^{4}$ ¶

Neighborhood

Every logical edge within two steps of this node.

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partly declared
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Edges

type	direction	node	provenance	where
`depends_on`	→	The plate energy	declared	appendices/A-long-proofs.tex:33344
`depends_on`	←	Why the operator comes out as $\nabla^{4}$	declared	appendices/A-long-proofs.tex:33386
`proves`	←	app:A-long-proofs@proof-407	declared	appendices/A-long-proofs.tex:33347