Finite-element method (32 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)

2. Rayleigh-Ritz procedure (cont'd)

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)

32 of 47

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

5. Assembly of system equation (cont'd)

(\begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{matrix}) (\begin{matrix} w_{1} \\ w_{2} \\ w_{3} \end{matrix}) = (\begin{matrix} f_{1} \\ f_{2} \\ f_{3} \end{matrix})

and

(\begin{matrix} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \\ b_{31} & b_{32} & b_{33} \end{matrix}) (\begin{matrix} w_{2} \\ w_{3} \\ w_{4} \end{matrix}) = (\begin{matrix} g_{2} \\ g_{3} \\ g_{4} \end{matrix}) .

(Eqn. 11)

Now, since the \(w_2\) and \(w_3\) in Equation 11 are the same for both elements, we can combine the two equations as follows:

$(\begin{matrix} a_{11} & a_{12} & a_{13} & 0 \\ a_{21} & a_{22} + b_{11} & a_{23} + b_{12} & b_{13} \\ a_{31} & a_{32} + b_{21} & a_{33} + b_{22} & b_{23} \\ 0 & b_{31} & b_{32} & b_{33} \end{matrix}) (\begin{matrix} w_{1} \\ w_{2} \\ w_{3} \\ w_{4} \end{matrix}) = (\begin{matrix} f_{1} \\ f_{2} + g_{2} \\ f_{3} + g_{3} \\ g_{4} \end{matrix}) .$ (Eqn. 12)

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

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