Next 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) 27 of 47 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

3. A simple element analysis (cont'd)

The natural-coördinate method (Desai & Abel, 1972, pp. 88-91) expresses the location of any point in the triangular element by the area coördinates \((\zeta_1, \zeta_2, \zeta_3)\), where \(\zeta_i = A_i / A\); \(A\) is the total area of the triangle and the \(A_i\) are as shown in the Figure. (Note that the three \(\zeta_i\) are not independent, since they add up to 1.) We can use the \(\zeta_i\) as the set of basis functions. It can be shown that in this case the coefficients \(c_i\) become the nodal displacements \(w_i\). Following the Rayleigh-Ritz procedure again leads to equation 10.

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R. Funnell
Last modified: 2018-11-07 12:52:06

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