theorem A.695 Boussinesq's point-force solution, quoted

open in the book · appendices/A-long-proofs.tex:33739 · p. 3130

Rests on

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 definition 7.126 Line and surface integrals ¶
      - depends_on definition 30.2 Representative volume element; continuum field ¶
    - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      - depends_on definition 30.17 Traction ¶ ↺
      - depends_on definition 13.5 Tensor under orthogonal transformations ¶
      - proves proof ch:13-continuum-elasticity@proof-7 ¶
    - 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 theorem 8.19 Fundamental theorem of algebra ¶
      - depends_on theorem 5.71 The eigenvalues are the roots of the characteristic polynomial ¶
      - proves proof ch:03-linear-algebra-representations@proof-27 ¶
    - depends_on definition 5.41 Adjoint ¶
      - depends_on definition 5.18 Inner product ¶
      - depends_on definition 5.37 Linear transformation ¶
    - depends_on theorem 5.40 Rank–nullity ¶
      - depends_on definition 5.15 Basis ¶
      - depends_on definition 5.39 Kernel, image, nullity, rank ¶
      - depends_on lemma 5.38 Exchange and completion ¶
      - proves proof ch:03-linear-algebra-representations@proof-13 ¶
    - 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 ¶ ↺
depends_on theorem 30.18 Cauchy: the stress tensor exists ¶ ↺

Supports

depends_on definition A.698 The Hertz contact problem ¶
- depends_on lemma A.700 The displacement produced by an elliptic pressure ¶
  - depends_on theorem A.702 Hertz's solution ¶
    - depends_on example A.703 The numbers of the chapter, recomputed ¶
    - depends_on remark A.704 $E^{*}$ in two roles, and one trap ¶
    - depends_on remark A.705 The dangerous stress is below the surface ¶
- depends_on proposition A.701 The two-body compliance rule ¶
  - depends_on theorem A.702 Hertz's solution ¶ ↺
- depends_on remark A.699 The third condition is not decoration ¶
- depends_on theorem A.702 Hertz's solution ¶ ↺
depends_on lemma A.697 Surface displacement under a distributed pressure ¶
- depends_on lemma A.700 The displacement produced by an elliptic pressure ¶ ↺
- depends_on proposition A.701 The two-body compliance rule ¶ ↺

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
`cites`	→	Theory of Elasticity	derived	appendices/A-long-proofs.tex:33752
`depends_on`	→	The engineering moduli	declared	appendices/A-long-proofs.tex:33755
`depends_on`	→	eq:elast-hooke-isotropic	declared	appendices/A-long-proofs.tex:33755
`depends_on`	→	Cauchy: the stress tensor exists	declared	appendices/A-long-proofs.tex:33755
`depends_on`	←	The Hertz contact problem	declared	appendices/A-long-proofs.tex:33844
`depends_on`	←	Surface displacement under a distributed pressure	declared	appendices/A-long-proofs.tex:33804