definition A.680 Kirchhoff kinematics

open in the book · appendices/A-long-proofs.tex:33082 · p. 3123

ground object -- no derivation owed

Rests on

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 30.31 The engineering moduli ¶
  - depends_on definition 30.20 Pressure and deviatoric stress ¶
    - depends_on proposition 30.19 The stress tensor is symmetric ¶
      - depends_on definition 30.17 Traction ¶
      - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      - proves proof ch:13-continuum-elasticity@proof-8 ¶
    - depends_on theorem 5.79 Spectral theorem for a self-adjoint operator ¶
      - depends_on corollary 5.72 Existence of an eigenvalue over $\C$ ¶
      - depends_on definition 5.41 Adjoint ¶
      - depends_on theorem 5.40 Rank–nullity ¶
      - proves proof ch:03-linear-algebra-representations@proof-31 ¶
  - depends_on equation 30.21 eq:elast-hooke-isotropic ¶
- depends_on equation 30.21 eq:elast-hooke-isotropic ¶ ↺
- proves proof ch:13-continuum-elasticity@proof-27 ¶

Supports

depends_on lemma A.687 Kinetic energy ¶
- depends_on theorem A.688 The Kirchhoff plate equation ¶
  - depends_on remark A.690 Poisson's count, and why it cannot be right ¶
  - depends_on theorem A.691 Kirchhoff's edge conditions and the corner force ¶
    - depends_on remark A.692 The corner force is real, and you can feel it ¶
depends_on lemma A.681 Strains under the Kirchhoff hypothesis ¶
- depends_on proposition A.684 The plate energy ¶
  - depends_on lemma A.685 The Gaussian-curvature term is a null Lagrangian ¶
    - depends_on remark A.686 Why the operator comes out as $\nabla^{4}$ ¶
  - depends_on theorem A.688 The Kirchhoff plate equation ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Linear strain and infinitesimal rotation	declared	appendices/A-long-proofs.tex:33097
`depends_on`	→	Moment and curvature	declared	appendices/A-long-proofs.tex:33097
`depends_on`	←	Kinetic energy	declared	appendices/A-long-proofs.tex:33402
`depends_on`	←	Strains under the Kirchhoff hypothesis	declared	appendices/A-long-proofs.tex:33112