Exact(28)
HENM and ANM basically solve an eigen-problem involving a 3 N ×3 N force constant matrix (the second derivatives of the potential, see below), the Hessian (H) that contains N × N super elements Hij (each super element is of dimension 3 ×3) The form is derived from the second derivatives (with respect to the node displacements) of the potential.
The word protean, one meaning of which is "changeable in shape or form," is derived from Proteus.
Its form is derived from the plan of a London housing estate, whose architects were themselves the distant inheritors of a utopian ideal, no matter how debased that ideal became.
Then, the following equivalent form is derived.
In Section 3.1, a general form is derived.
First, the force displacement relation in total form is derived.
Similar(32)
The oldest is the beam and girder system, whose form was derived from wood and steel construction: slabs rest on beams, beams rest on girders, and girders rest on columns in a regular pattern.
However, to be comprehensive, the MFEM in non-hierarchical p-refinement form was derived.
The resulting equations of motion in matrix form are derived by using Hamilton's principle.
Solutions in an explicit form are derived for two limiting cases, and the corresponding validity conditions presented.
For beams with a linear relationship between the cross-sectional moment of inertia and area optimal shapes of analytical form are derived.
Write better and faster with AI suggestions while staying true to your unique style.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com