7.3: List of Symbols
- Page ID
- 44558
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)| \(A\) | area, free energy, Madelung constant |
| A | transformation matrix |
| \(\mathcal{A}\) | plate extensional stiffness |
| \(a\) | length, transformation matrix, crack length |
| \(a_T\) | time-temperature shifting factor |
| \(B\) | design allowable for strength |
| B | matrix of derivative of interpolation functions |
| \(\mathcal{B}\) | plate coupling stiffness |
| \(b\) | width, thickness |
| \(C\) | stress optical coefficient, compliance |
| \(\mathcal{C}\) | viscoelastic compliance operator |
| \(c\) | numerical constant, length, speed of light |
| C.V. | coefficient of variation |
| D | stiffness matrix, flexural rigidity of plate |
| \(\mathcal{D}\) | plate bending stiffness |
| \(d\) | diameter, distance, grain size |
| \(E\) | modulus of elasticity, electric field |
| \(E^*\) | activation energy |
| \(\mathcal{E}\) | viscoelastic stiffness operator |
| \(e\) | electronic charge |
| \(e_{ij}\) | deviatoric strain |
| \(F\) | force |
| \(f_s\) | form factor for shear |
| \(G\) | shear modulus |
| \(\mathcal{G}\) | viscoelastic shear stiffness operator |
| \(\mathcal{G}_c\) | critical strain energy release rate |
| \(g\) | acceleration of gravity |
| GF | gage factor for strain gages |
| \(H\) | Brinell hardness |
| \(h\) | depth of beam |
| \(I\) | moment of inertia, stress invariant |
| I | identity matrix |
| \(J\) | polar moment of inertia |
| \(K\) | bulk modulus, global stiffness matrix, stress intensity factor |
| \(\mathcal{K}\) | viscoelastic bulk stiffness operator |
| \(k\) | spring stiffness, element stiffness, shear yield stress, Boltzman's constant |
| \(L\) | length, beam span |
| L | matrix of differential operators |
| \(M\) | bending moment |
| \(N\) | crosslink or segment density, moire fringe number, interpolation function, cycles to failure |
| N | traction per unit width on plate |
| \(N_A\) | Avogadro's number |
| \(\mathcal{N}\) | viscoelastic Poisson operator |
| \(n\) | refractive index, number of fatigue cycles |
| \(\hat{n}\) | unit normal vector |
| \(P\) | concentrated force |
| \(P_f\) | fracture load, probability of failure |
| \(P_s\) | probability of survival |
| \(p\) | pressure, moire gridline spacing |
| \(Q\) | force resultant, first moment of area |
| \(q\) | distributed load |
| \(R\) | radius, reaction force, strain or stress rate, gas constant, electrical resistance |
| R | Reuter's matrix |
| \(r\) | radius, area reduction ratio |
| \(S\) | entropy, moire fringe spacing, total surface energy, alternating stress |
| S | compliance matrix |
| \(s\) | Laplace variable, standard deviation |
| SCF | stress concentration factor |
| \(T\) | temperature, tensile force, stress vector, torque |
| \(T_g\) | glass transition temperature |
| \(t\) | time, thickness |
| \(t_f\) | time to failure |
| \(U\) | strain energy |
| \(U^*\) | strain energy per unit volume |
| UTS | ultimate tensile stress |
| \(\tilde{u}\) | approximate displacement function |
| \(V\) | shearing force, volume, voltage |
| \(V^*\) | activation volume |
| \(v\) | velocity |
| \(W\) | weight, work |
| \(u, v, w\) | components of displacement |
| \(x, y , z\) | rectangular coordinates |
| \(X\) | standard normal variable |
| \(\alpha, \beta\) | curvilinear coordinates |
| \(\alpha_L\) | coefficient of linear thermal expansion |
| \(\gamma\) | shear strain, surface energy per unit area, weight density |
| \(\delta\) | deflection |
| \(\delta_{ij}\) | Kroenecher delta |
| \(\epsilon\) | normal strain |
| \(\mathcal{\epsilon}\) | strain pseudovector |
| \(\epsilon_{ij}\) | strain tensor |
| \(\epsilon_T\) | thermal strain |
| \(\zeta\) | viscosity |
| \(\theta\) | angle, angle of twist per unit length |
| \(\kappa\) | curvature |
| \(\lambda\) | extension ratio, wavelength |
| \(\nu\) | Poisson's ratio |
| \(\rho\) | density, electrical resistivity |
| \(\sum_{ij}\) | distortional stress |
| \(\sigma\) | normal stress |
| \(\mathcal{\sigma}\) | stress pseudovector |
| \(\sigma_{ij}\) | stress tensor |
| \(\sigma_e\) | endurance limit |
| \(\sigma_f\) | failure stress |
| \(\sigma_m\) | mean stress |
| \(\sigma_M\) | Mises stress |
| \(\sigma_t\) | true stress |
| \(\sigma_Y\) | yield stress |
| \(\tau\) | shear stress, relaxation time |
| \(\phi\) | Airy stress function |
| \(\xi\) | dummy length or time variable |
| \(\Omega\) | configurational probability |
| \(\omega\) | angular frequency |
| \(\nabla\) | gradient operator |