Index
A
Analytical solution
Euler–Bernoulli beam, 37, 38
rod, 11
Timoshenko beam, 92
Antiderivatives, 153
B
Backward difference scheme, 3
Bar. see rod
Basic equations
Euler–Bernoulli beam, 39
rod, 12
Timoshenko beam, 90
Bending stiffness, 41, 105
Boundary conditions
Euler–Bernoulli beam, 41
rod, 13
Timoshenko beam, 93
C
Centered difference scheme, 2
Centered Euler. see centered difference
Centroid, 155
Collocation method, 4
D
Derivative, 1
Differential equation, 1
Dirac delta function, 4, 6
E
Equivalent nodal force, 15, 42
Euler–Bernoulli beam, 37
basic equations, 39
boundary conditions, 41
definition, 37
internal reactions, 40
partial differential equation, 40
F
Fictitious node, 16, 26, 27, 29, 30, 33, 47
Finite difference approximations, 5
Finite difference method, 1
Finite element method, 1, 103
First moment of area, 155
Forward difference scheme, 3
G
Grid points. see nodes
H
Hooke’s law, 13, 40
I
Ideal plastic, 103
Infinite series. see Taylor’s series
Integral
definite, 153
indefinite, 153
Internal bending moment, 38, 39, 92
Internal normal force, 11, 13
Internal shear force, 38, 39, 92
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
A. Öchsner, Structural Mechanics with a Pen,
https://doi.org/10.1007/978-3-030-65892-2
159