Design and Nonlinear Closed-Form Displacement Expressions of Low Stiffness Lattice Truss Beam Structures

摘要

Four classes of low stiffness lattice truss beam structures and a deterministic methodology for deriving governing closed-form displacement expressions for each class are presented. Each class consist of an infinite series of progressively lower stiffness lattice truss beam designs. Derived displacement expressions per class are shown to consist of a series of polynomial, exponential, and/or trigonometric functions. Low stiffness lattice truss beams have the general geometry of classic Euler-Bernoulli beams however they don't exhibit classic 2~(nd) degree axial or 4th degree bending polynomial displacement behavior under a uniform load. The analysis methodology utilizes lattice design, finite element analysis, Castigliano's second theorem, and mathematical extrapolation to generate highly accurate closed-form lattice displacement expressions. Beam stiffness parameters can be obtained from the resulting displacement expressions. The study provides fundamental insight into the significantly larger domain of nonlinear low stiffness elastic lattice truss beam structures relative to classic ruler Bernoulli linear elastic beams. Low stiffness lattice truss beam designs and displacement expressions have potential application within the new disciplines of smart metamaterials and structures, advanced finite element analysis tools, damage tolerant truss design, piezoelectric technology, and fractal theory.