INDEX

  1.  
  2. Absolute coordinates
  3. Absolute nodal coordinate formulation
    1. coupled deformation modes
  4. Acceleration
  5. Air pressure
  6. Almansi strains
  7. ANCF geometry
  8. ANCF surfaces
  9. ANCF-coupled deformation modes
  10. Angular acceleration
  11. Angular momentum
  12. Angular velocity
  13. Anisotropic linearly elastic material
  14. Approximation methods
    1. classical, finite–element method, Rayleigh–Ritz method
    2. Finite element method see Finite element method
    3. Rayleigh–Ritz method see Rayleigh–Ritz method
  15. Arc length
  16. Area change
  17. Associative flow rule see Associative plasticity
  18. Associative plasticity
  19. Assumed displacement field
  20. Assumed strain element
  21. Assumed stress element
  22. Axis of rotation
  23.  
  24. Back stress
  25. Backward implicit Euler method
  26. Basis functions
  27. Bauschinger effect
  28. Beam elements
    1. three-dimensional
  29. Beam elements (Continued)
    1. two-dimensional
  30. Beam theory
  31. Bernstein polynomials
  32. Bezier geometry
  33. Bezier method
  34. Binomial vector
  35. Biot stress
  36. Blending functions see Basis functions
  37. Body(s)
    1. coordinate system
    2. force
    3. reference
    4. rigid
  38. Boolean matrix
  39. Breakpoints
  40. B-spline
    1. surfaces
  41. Bulk modulus
  42. Bulk viscosity coefficient
  43.  
  44. Cable element
  45. CAD
  46. Cartesian tensor
  47. Cauchy
    1. elastic material
    2. first law of motion
    3. second law of motion
    4. strain
    5. stress
      1. 97
  48. Cauchy stress formula
  49. Cauchy–Green deformation tensor
    1. left
    2. right
  50. Cayley-Hamilton theorem
  51. Center of mass
  52. Change of parameters
  53. Characteristic equation
  54. Characteristic values see Eigenvalues
  55. Chebyshev polynomials
  56. Cholesky coordinates
  57. Chord frame
  58. Classical theories
  59. Component mode techniques
  60. Computational geometry
  61. Computer Aided Design see CAD
  62. Connectivity conditions
  63. Conservation of mass
  64. Consistency condition see Persistency condition
  65. Consistency parameter
  66. Consistent mass
  67. Constitutive equations
  68. Constitutive integration algorithm
  69. Continuity equation
  70. Continuum forces
  71. Control points
  72. Control polygon
  73. Control volume
  74. Convective stress rate
  75. Convective term
  76. Convolution integral see Duhamel integral
  77. Coordinate reduction
  78. Coordinate transformation
  79. Co-rotational frame
  80. Coupled deformation modes see ANCF-coupled deformation modes
  81. Creep function
  82. Curvature
    1. Gaussian
    2. mean
    3. normal
    4. principal
    5. radius of
    6. surface
    7. vector
  83. Curved beams
  84. Curved configuration
  85. Curved geometry
  86. Curved structure
  87. Curves
    1. theory
  88.  
  89. D'Alembert's principle
  90. deCasteljau algorithm
  91. Decomposition of displacement
  92. Deformation examples
  93. Deformation measures
  94. Deviatoric stresses
  95. Dilatation
  96. Direction cosines
  97. Discontinuities
    1. non-structural
    2. structural
  98. Discrete equations
  99. Displacement
    1. axial
    2. bending
    3. decomposition
    4. field
    5. fluid
    6. general
    7. gradients
    8. homogeneous
    9. isochoric
    10. modes
    11. nodal
    12. planar
    13. reference
    14. rigid-body
    15. transverse
      1. 228
    16. virtual
  100. Dissipation
  101. Divergence operator
  102. Divergence theorem
  103. Double product
  104. Duhamel integral
  105. Dummy index
  106. Dyadic product see Outer product
  107. Dynamic coupling see Inertia coupling
  108.  
  109. Eigenvalue analysis
  110. Eigenvalue problem
  111. Eigenvalues
  112. Eigenvectors
  113. Elastic coefficients
  114. Elastic coordinates
  115. Elastic energy
  116. Elastic force
    1. power
  117. Elastic limit
  118. Elastic line approach
  119. Elastic loading
  120. Elastic mid-surface approach
  121. Elastic predictor
  122. Elasto-plastic tangent modulus
  123. Embedding technique
  124. Energy
    1. balance
    2. elastic
    3. kinetic
    4. strain
  125. Engineering strain
  126. Equations of equilibrium
  127. Equations of motion
    1. for deformable bodies
    2. for fluids
    3. for particles
    4. for rigid bodies
  128. Equilibrium
    1. equations of
    2. force
  129. Equivalent plastic strain
  130. Euler angles
    1. singularity
    2. transformation matrix in terms of
  131. Euler equation
  132. Euler parameters
  133. Euler–Bernoulli beam
  134. Eulerian coordinates
  135. Eulerian description
  136. Eulerian formulation
  137. Eulerian strain
  138. Evolution equations
  139. Extension
  140.  
  141. Finite difference method
  142. Finite dimensional model
  143. Finite element
    1. assumed displacement
    2. assumed strain
    3. assumed stress
    4. beam
    5. Boolean matrix
    6. brick
    7. cable
    8. connectivity conditions
    9. formulation
    10. generalized forces
    11. gradient deficient
    12. inertia shape integrals
    13. intermediate coordinate system
    14. isoparametric
    15. large deformation
    16. mass matrix
    17. method
    18. nodal coordinates
    19. performance
    20. plate
    21. rectangular
    22. reference conditions
    23. shape function
    24. shear deformable
    25. solid
    26. stiffness matrix
    27. subparametric
    28. superparametric
    29. tetrahedral
    30. triangular
  144. Finite rotation
  145. First fundamental form of surfaces
    1. coefficients of
  146. First Piola-Kirchhoff stress tensor
  147. Floating frame of reference
  148. Flow rule
  149. Flow stress
  150. Fluid
    1. constitutive equations
    2. ideal
    3. incompressible
    4. inviscid
    5. isotropic
    6. Newtonian
  151. Force
    1. body
    2. continuum
    3. elastic
    4. gravitational
    5. inertia
    6. magnetic
    7. pressure
    8. surface
  152. Frame indifference
  153. Free index
  154. Frenet frame
  155. Fundamental forms
    1. first
    2. second
  156.  
  157. Gauss quadrature
  158. Gauss theorem
  159. Gaussian curvature
  160. Gauss-Legendre coefficients
  161. General displacement
  162. Generalized forces
  163. Generalized Newton–Euler equations
  164. Geometric interpretation of strains
  165. Geometry see Computational geometry
  166. Gradient coordinates
  167. Gradient deficient finite element
  168. Gradient of the displacement vector
  169. Gravitational force
  170. Green elastic material
  171. Green-Lagrange strain tensor
  172. Green–Naghdi stress rate
  173.  
  174. Hardening
    1. isotropic
    2. kinematic
    3. linear
    4. nonlinear
    5. strain
  175. Hellinger-Reissner principle
  176. Hermite polynomials
  177. Homogeneous displacement
  178. Homogeneous material
  179. Homogeneous motion
  180. Hookean material
  181. Hooke's law
  182. Hourglass modes
  183. Householder transformation
  184. Huber-von Mises yield function
  185. Hu-Washizu principle
  186. Hybrid principles see Multifield variational principles
  187. Hydrostatic pressure
  188. Hyperelastic material
  189. Hyperelastic potential
  190. Hyperelastic-plastic material
  191. Hypoelastic material
  192.  
  193. I-CAD-A
  194. Ideal fluid
  195. Impulse response function
  196. Incompressibility
  197. Inelastic material
  198. Inertia
    1. coupling
    2. force
    3. mass moment of
    4. shape integrals
    5. tensor
  199. Infinitesimal rotation
  200. Infinitesimal strains
  201. Intermediate element coordinate system
  202. Intermediate plastic configuration
  203. Internal variables
  204. Interpolating polynomial
  205. Invariants
    1. strain
    2. stress
    3. tensor
  206. Inviscid flow
  207. Irrotational flow
  208. Isochoric displacement
  209. Isoparametric property
  210. Isotropic fluid
  211. Isotropic hardening
  212. Isotropic material
  213. Isotropic plastic modulus
  214.  
  215. J2 flow theory
    1. isotropic/kinematic hardening
  216. Jacobian matrix
  217. Jaumann stress rate
  218.  
  219. Kelvin viscoelastic model
  220. Kinematic analysis
  221. Kinematic equations
  222. Kinematic hardening
    1. modulus
  223. Kinematic viscosity
  224. Kinematics
    1. of deformable bodies
    2. of rigid bodies
  225. Kirchhoff stress
  226. Knot insertion
  227. Knot multiplicity
  228. Knot vector
  229. Kronecker delta
  230. Kuhn-Tucker complementarity condition
  231.  
  232. Lagrange multipliers
  233. Lagrange-D'Alembert equation
  234. Lagrangian coordinates
  235. Lagrangian description
  236. Lagrangian formulation
    1. total
    2. updated
  237. Lagrangian strain tensor see Green-Lagrange strain tensor
  238. Lame's constants
  239. Laquerre polynomials
  240. Large deformation problem
  241. Large rotation
  242. Leaf spring, (AU: Not found)
  243. Left Cauchy-Green strain tensor
  244. Left stretch tensor
  245. Legendre
    1. coefficients
    2. polynomials
  246. Linear momentum
  247. Linear structural systems
  248. Linear theory of elastodynamics
  249. Liquid sloshing
  250. Loading and unloading conditions
  251. Locking
    1. membrane
    2. shear
    3. volumetric
  252. Logarithmic strain
  253. Lumped mass
  254.  
  255. Magnetic force
  256. Mass
    1. center of
    2. conservation of
    3. consistent
    4. lumped
    5. matrix
    6. moment of inertia
  257. Material
    1. anisotropic
    2. Cauchy elastic
    3. coordinates
    4. Green elastic
    5. homogeneous
    6. Hookean
    7. hyperelastic
    8. hypoelastic
    9. incompressible
    10. inelastic
    11. isotropic
    12. Mooney-Rivlin
    13. Neo-Hookean
    14. symmetry
    15. viscoelastic
  258. Matrix
    1. addition
    2. adjoint
    3. associative law
    4. cofactor
    5. determinant
    6. diagonal
    7. displacement vector gradients
    8. elastic coefficients
    9. identity
    10. inverse
    11. mass
    12. minor
    13. multiplication
    14. null
    15. orthogonal
    16. position vector gradients
    17. product
    18. projection
    19. rectangular
    20. singular
    21. skew symmetric
    22. square
    23. stiffness
    24. symmetric
    25. trace
    26. transpose
    27. unit
    28. zero
  259. Maxwell viscoelastic model
  260. Mean curvature
  261. Mean surface traction
  262. Mechanics
    1. particles
    2. rigid bodies
  263. Membrane locking
  264. Mixed principles see Multi-field variational principles
  265. Modal coordinates
  266. Modal transformation
  267. Mode shapes
  268. Modulus of elasticity see Young's modulus
  269. Modulus of rigidity
  270. Mohr's circle
  271. Moment of inertia
  272. Momentum
  273. Mooney-Rivlin material
  274. Motion description
  275. Multibody computer programs
    1. flexible
  276. Multibody system
  277. Multi-field variational principles
  278. Multiplicative decomposition
  279.  
  280. Nanson's formula
  281. Natural strain
  282. Navier-Stokes equations
  283. Neo-Hookean material
  284. Neutral loading
  285. Newton equation
  286. Newton-Cotes formulas
  287. Newton–Euler equations
  288. Newton-Euler formulation
  289. Newtonian fluid
  290. Newtonian viscous fluid
  291. Newton's second law
  292. Nodal
    1. coordinates
    2. points
  293. Nonconservative system
  294. Nonhomogeneous motion
  295. Non-incremental solution
  296. Nonstructural discontinuities
  297. Normal curvature
  298. Normal strain
  299. Normal stress
  300. Numerical Solution
    1. plasticity equations
  301. NURBS
  302.  
  303. Objectivity
  304. Oldroyd stress rate
  305. Orthogonal matrix
  306. Orthogonal transformation
    1. improper
    2. proper
  307. Osculating plane
  308. Outer product
  309. Overstress function
  310.  
  311. Parallel axis theorem
  312. Partial differential equations of equilibrium
  313. Partial stress
  314. Particle mechanics
  315. Patch test
  316. Penalty method
  317. Perfect plasticity
  318. Persistency condition
  319. Physical stress see True stress
  320. Piola transformation
  321. Piola-Kirchhoff stress
  322. Pitch angle
  323. Planar analysis
  324. Planar motion
  325. Plane strain
  326. Plane stress
  327. Plastic corrector
  328. Plastic flow rule
  329. Plastic loading
  330. Plastic strain
  331. Plasticity
    1. associative
    2. equations
    3. explicit solution
    4. formulations
    5. implicit solution
    6. nonassociative
    7. perfect
    8. rate dependent
    9. small strain
  332. Plate element
    1. thin
  333. Point coordinates
  334. Poisson effect
  335. Poisson's ratio
  336. Polar decomposition theorem
  337. Position vector gradients, see also Matrix of position vector gradients
  338. Power basis
  339. Prager-Ziegler rule
  340. Principal axes
  341. Principal curvatures
  342. Principal directions
  343. Principal strain
  344. Principal stress
  345. Principal values
  346. Principle of conservation of mass
  347. Principle of virtual work
  348. Projection
    1. Matrix
  349. Prony series
  350. Proportional limit
  351. Pullback
  352. Push-forward
  353.  
  354. QR decomposition
  355. Quadrature
  356.  
  357. Radius of curvature
  358. Rate independent material
  359. Rate of deformation
  360. Rate-dependent
    1. material
    2. plasticity
  361. Rayleigh–Ritz method
  362. Rectangular element
  363. Reduced integration
    1. selective
  364. Redundant coordinates
  365. Reference conditions
  366. Reference coordinate system
  367. Reference coordinates
  368. Reference motion
  369. Reflection
  370. Relaxation function
  371. Relaxation time
  372. Return mapping algorithm
    1. radial
  373. Reynolds' transport theorem
  374. Right Cauchy-Green strain tensor
  375. Right stretch tensor
  376. Rigid body
    1. dynamics
    2. inertia
    3. kinematics
    4. mass matrix
    5. motion
    6. planar motion
    7. translation
  377. Rodriguez formula
  378. Rodriguez parameters
  379. Roll angle
  380. Rotation
    1. field
    2. finite
    3. infinitesimal
    4. large
    5. matrix
  381.  
  382. Scalar triple product
  383. Second fundamental form of surfaces
    1. coefficients of
  384. Second Piola-Kirchhoff stress tensor
  385. Selective reduced integration
  386. Separation of variables
  387. Shape function
    1. matrix
  388. Shear
    1. deformation
    2. locking
    3. modulus
    4. strain
    5. stress
    6. viscosity coefficient
  389. Shells
  390. Simpson's rule
  391. Singular point
  392. Slider crank mechanism
  393. Slip rate
  394. Sloshing
  395. Small deformation
  396. Small strains see Infinitesimal strains
  397. Solid element
  398. Spatial coordinates
  399. Spectral decomposition
  400. Spin
    1. tensor
  401. Spurious singular modes
  402. Standard viscoelastic model
  403. Stiffness matrix
  404. Stokes' relation
  405. Strain
    1. Almansi
    2. auxiliary strain energy density function
    3. Cauchy
    4. components
    5. energy
    6. engineering
    7. Eulerian
    8. Geometric interpretation
    9. Green–Lagrange
    10. hardening
    11. infinitesimal
    12. invariants
    13. logarithmic
    14. natural
    15. normal
    16. plane
    17. principal
    18. shear
    19. small see Infinitesimal strains
    20. space formulation
    21. transformation
    22. vector
    23. volumetric
  406. Strain additive decomposition
  407. Strain-displacement relationships see Constitutive equations
  408. Stress
    1. back
    2. Biot
    3. Cauchy
      1. 97
    4. components
    5. deviatoric
    6. invariants
    7. Kirchhoff
    8. measures
    9. normal
    10. physical interpretation
    11. Piola-Kirchhoff
    12. plane
    13. principal
    14. rate
    15. shear
    16. space formulation
    17. symmetry
    18. transformation
    19. true
    20. update algorithm
    21. vector
  409. Stress–strain relationships see Constitutive equations
  410. Stretch
    1. Left
    2. Right
    3. tensor
  411. Structural applications
  412. Structural discontinuities
  413. Structural systems
  414. Subparametric finite element
  415. Summation convention
  416. Superparametric finite element
  417. Surface
    1. curvature
    2. elliptic
    3. hyperbolic
    4. parabolic
    5. planar
    6. theory
  418. Surface force
  419. Surface traction
  420. Symmetry of the stress tensor
  421.  
  422. Tangent elastoplastic modulus
  423. Tangent frame
  424. Tank car
  425. Tensor
    1. Almansi strain
    2. alternating
    3. antisymmetric
    4. Cartesian
    5. Cauchy strain
    6. contraction
    7. double product
    8. Eulerian strain
    9. Fourth-order
    10. Green-Lagrange strain
    11. higher order
    12. identity
    13. infinitesimal strain
    14. invariants
    15. isotropic
    16. left Cauchy-Green strain
    17. rate of deformation
    18. right Cauchy-Green strain
    19. second order
    20. skew symmetric
    21. spherical
    22. spin
    23. symmetric
    24. third order
    25. unit see Identity tensor
    26. velocity gradient
  426. Theory of curves
  427. Theory of surfaces
  428. Thin plate element
  429. Tire
  430. Torsion
  431. Total Lagrangian formulation
  432. Trace of matrix
  433. Traction
  434. Transformation matrix
    1. planar
    2. spatial
    3. in terms of Euler angles
  435. Translation
  436. Transport term
  437. Transpose of matrix
  438. Tresca yield function
  439. Triadic product
  440. Trial stress
  441. Triangular element
  442. Triple product
  443. True stress
  444. Truesdell stress rate
  445.  
  446. Unit dyads
  447. Updated Lagrangian formulation
  448.  
  449. Vector
    1. cross product
    2. dot product
    3. dyadic product
    4. inner product
    5. length of
    6. norm of
    7. orthogonal
    8. outer product
    9. scalar product
    10. unit
  450. Velocity
    1. angular
    2. field
    3. gradient
    4. strain
    5. transformation
    6. virtual
  451. Virtual displacement
  452. Virtual power principle
  453. Virtual velocity
  454. Virtual work
    1. of applied forces
    2. of elastic forces
    3. of inertia forces
    4. principle
  455. Viscoelastic material
    1. Kelvin model
    2. linear
    3. Maxwell model
    4. nonlinear
    5. one-dimensional model
    6. standard model
    7. strain additive decomposition
    8. Voigt model
  456. Viscosity coefficient
  457. Voigt viscoelastic model
  458. Volume change
  459. Volumetric locking
  460. Volumetric strain
  461. von Mises effective stress
  462. von Mises yield function
  463. Vorticity
  464.  
  465. Weak form
  466. Weight
    1. coefficients
    2. factors
  467. Work and energy
    1. principle
  468.  
  469. Yaw angle
  470. Yield condition
  471. Yield criterion
  472. Yield function
    1. Huber-von Mises
    2. Tresca
    3. von Mises
  473. Yield stress
  474. Young's modulus
  475.  
  476. Zero energy modes
  477. Ziegler's rule
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