Energy analysis of continuum elastic structures by the generalized finite-volume theory

TOP2DFVT: An Efficient Matlab Implementation for Topology Optimization based on the Finite-Volume Theory

“…Additionally, the differential equilibrium equations are locally satisfied in an average-sense (Araujo et al, 2021), and the displacement field in the subvolume is modeled by secondorder polynomials defined in local coordinates (Cavalcante et al, 2007a). The presented formulation has its roots in the standard version of the finite-volume theory presented in Cavalcante and Pindera (2012a) for structured meshes formed by rectangular subvolumes.…”

“…Additionally, the surface-averaged tractions are not energetically conjugated with the surface-averaged displacements along the subvolume faces, which leads the 𝑲 (𝑞) matrix to be more a pseudo stiffness matrix. Following Araujo et al (2021), it can be defined a modified local system of equations in terms of resultant forces acting in the edges of a subvolume 𝑞, which are energetically conjugated with the surface-averaged displacements, as follows…”

“…According to Araujo et al (2021), the total work done by external loadings and the total strain energy of a deformed structure are equal for quasi-static analysis in the context of the standard finite-volume theory. As a result, the nested topology optimization problem for compliance minimization can be written as…”

“…Numerical stability is an essential feature of the finitevolume theory applied in topology optimization tools to obtain more reliable optimized topologies. Also, this technique has shown to be well suitable method for elastic stress analysis in solid mechanics, investigations of its numerical efficiency can be found in Araujo et al (2021), Cavalcante et al (2007aCavalcante et al ( ,b, 2008 and Cavalcante and Pindera (2012a,b). The satisfaction of equilibrium equations at the subvolume level, concomitant to kinematic and static continuities established in a surface-averaged sense between common faces of adjacent subvolumes, are features that distinguish the finite-volume theory from the finite-element method.…”