Finite-element method (14 of 47)

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1. Introduction

1. Introduction (cont'd)

1. Introduction (cont'd)

1. Introduction (cont'd)

1. Introduction (cont'd)

1. Introduction (cont'd)

1. Introduction (cont'd)

1. Introduction (cont'd)

2. Rayleigh-Ritz procedure

2. Rayleigh-Ritz procedure (cont'd)

2. Rayleigh-Ritz procedure (cont'd)

2. Rayleigh-Ritz procedure (cont'd)

2. Rayleigh-Ritz procedure (cont'd)

14 of 47

2. Rayleigh-Ritz procedure (cont'd)

2. Rayleigh-Ritz procedure (cont'd)

2. Rayleigh-Ritz procedure (cont'd)

3. A simple element analysis

3. A simple element analysis (cont'd)

3. A simple element analysis (cont'd)

3. A simple element analysis (cont'd)

3. A simple element analysis (cont'd)

3. A simple element analysis (cont'd)

3. A simple element analysis (cont'd)

3. A simple element analysis (cont'd)

3. A simple element analysis (cont'd)

3. A simple element analysis (cont'd)

4. Higher-order elements

4. Higher-order elements (cont'd)

5. Assembly of system equation

5. Assembly of system equation (cont'd)

5. Assembly of system equation (cont'd)

5. Assembly of system equation (cont'd)

5. Assembly of system equation (cont'd)

6.1 Static problem

6.2 Undamped dynamic problem

6.2 Undamped dynamic problem (cont'd)

6.2 Undamped dynamic problem (cont'd)

6.2 Undamped dynamic problem (cont'd)

6.3.1 Modal analysis

6.3.1 Modal analysis (cont'd)

6.3.2 Time-domain analysis

6.3.2 Time-domain analysis (cont'd)

6.3.2 Time-domain analysis (cont'd)

6.3.2 Time-domain analysis (cont'd)

6.3.2 Time-domain analysis (cont'd)

6.3.3 Complex-valued analysis

2. Rayleigh-Ritz procedure (cont'd)

The linear combinations can be expressed as

$w (x) = \sum_{i = 1}^{n} c_{i} w_{i} (x)$
(Eqn. 1)
where the \(c_i\) are \(n\) constants defining \(w(\mathbf{x})\).

Since each of the basis functions is admissible, every function in the space of linear combinations will also be admissible.

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Last modified: 2018-11-07 12:52:06

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