Truss Mechanics
Radiation, Heat Transfer
In general, the radiation solution is temperature raised to the 4th degree. Hence, we seek a planar lattice truss design which generates a 4th degree polynomial solution when a perpendicular force is applied. The wireframe design presented in the nonlinear planar lattices section somewhat meets this requirement. The wireframe design solution with a center point force is a 3rd degree polynomial. Uniquely, the displacement solution for a perpendicular center force is also a 3rd degree polynomial. Therefore it is assumed that a perpendicular distributed force would generate the desired 4th degree displacement solution.
B.C. Clamped Clamped
Top View
Apply a distributed force and solve for center displacement. The member forces are similar too the planar wireframe forces due to a center force. You should generate a 4th degree solution.
Displacement?
Displacement?
Perspective View
Wireframe Design and Analysis Related to Radiation
Caution: Copious notes from 3 designs and derivations are presented. You can compare the displacement equations to classic continuum heat transfer convection equations. Consider the left end applied force as the heat source and the right end as one of three boundary conditions. This is a complex derivation, think 3rd year of engineering college or grad school level.