Finite-element method (8 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)

8 of 47

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)

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

1. Introduction (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})

The result of the analysis of a typical element type is a small matrix relating a vector of nodal displacements to a vector of applied nodal forces.

The components of the matrix can be expressed as functions of the shape and properties of the element, and the values of the components for a particular element can then be obtained by substituting the appropriate shape and property parameter values into the formulæ.

Once the element matrices have been calculated, they are all combined together into one large matrix representing the whole complex system, as discussed in Section 4.

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

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