Dynamic Animation of Stress Modes via the Integrated Force Method of Structural Analysis

Compatibility Condition in Theory of Solid Mechanics (Elasticity, Structures, and Design Optimization)

“…The animation of the stress mode shape in IFM/IFMD (ref. 22) detected a stress concentration region in the same blade due to a small hole, which is qualitatively shown in figure 8(a). Typically, stress mode shape is not available in the stiffness formulation.…”

“…The IFM element (ref. 22) used a total of 18 force unknowns: 4 for each normal stress and 2 for each shear stress. The brick element of a commercial code was comparable to the stiffness method of the IFM/Analyzers software.…”

Significance of Strain Formulation in Theory of Solid Mechanics

“…The three BCC given by equation (11) CBMF is defined through the EE and the CC in the field and on the boundary of an elastic continuum, given by equations (8) to (11). Stress determination by CBMF does not require the displacement boundary conditions.…”

“…11,16,17 Results for a few typical examples obtained using the IFM/Analyzers code and a commercial stiffness method code are depicted in figure 5. The three IFM elements used are (1) a four-node QUAD0405 membrane element with five force unknowns, (2) an eight-node brick element HEX0818 with 18 force unknowns, and (3) a fournode-plate bending element PLB0409 with nine unknown moments.…”

“…Research is in progress to alleviate the deficiency in the theory of solid mechanics. Benefits from the use of the completed strain formulation are being shown in continuum elasticity, [1][2][3][4][5][6] in finite element analysis, [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and in design optimization. [26][27][28][29][30][31][32][33][34][35][36] The theory of strengths of materials began with the cantilever experiment conducted by Galileo in 1632.…”