A simplified approach to the topology optimization of structures in case of unilateral material/supports

A simplified method to cope with the topology optimization of truss–like structures in case of unilateral behavior of material or supports is presented. The conventional formulation for volume–constrained compliance minimization is enriched with a set of stress constraints that enforce a suitable version of the Drucker–Prager strength criterion in order to prevent the arising of tensile (or compressive) members in the whole domain or within limited regions in the vicinity of the supports. The adopted numerical framework combines an ad hoc selection strategy along with the use of aggregation techniques that succeed in driving the energy–based minimization towards feasible designs through the enforcement of a limited number of stress constraints. Numerical simulations assess the proposed optimization framework in comparison with methods that are based on a full non–linear modeling of unilateral material/supports. An extension to the safety analysis of structures made of no–tension material is also highlighted

Comparative Study on the Optimal Topologies

The topology optimization is a leading tool in structural design. Due to the rapidly spreading need of the industry, commercial software are available in the market. Generally, these software are suitable for solving one subtask (preprocessing, postprocessing, stress calculation, etc.) but need some user manipulation to interconnect to one that is better for some other subproblem. This is the reason why we write a study on the available software and make suggestions on their usability. The purpose of this research is to briefly introduce selected software such as Rhino 3D, Grasshopper, Peregrine, Karamba, Galapagos, polyTop and PolyStress using topology optimization theory. Due to the demand to apply them for industrial applications, the additional goal is to make suggestions to make these software programs more user-friendly and to create algorithms to connect with software used in the industry, such as Consteel. This work also discusses the connected algorithms and optimization methods such as layout optimization by Peregrine, and topology optimization by polyTop and PolyStress. Several illustrative videos are provided as supplements. In addition to the text of this paper one can see demonstrations of the applications by the use of the provided YOUTUBE links

A numerical approach to the design of gridshells for WAAM

A novel approach based on funicular analysis is investigated to cope with the design of spatial truss networks fabricated by Wire-and-Arc Additive Manufacturing (WAAM). The minimization of the horizontal thrusts of networks with fixed plan geometry is stated both in terms of any independent subset of the force densities and in terms of the height of the restrained nodes. Local enforcements are formulated to prescribe lower and upper bounds for the vertical coordinates of the nodes, and to control the stress regime in the branches. This allows also for a straightforward control of the length and maximum force magnitude in each branch. Constraints are such that sequential convex programming can be conveniently exploited to handle grids with general topology and boundary conditions. Optimal networks for WAAM are preliminary investigated, accounting for different sets of the above prescriptions

Material-informed topology optimization for Wire-and-Arc Additive Manufacturing

Wire-and-Arc Additive Manufacturing (WAAM) is a metal 3d printing technique that allows fabricating elements ranging from simple geometry to extremely complex shapes. “Layer-by-layer” manufacturing produces a printed material with significant elastic anisotropy, whereas “dot-by-dot” printing may be used to fabricate funicular geometries in which the mechanical properties of the single bars are affected by the printing process. The design of WAAM components is addressed by formulating problems of structural optimizations that account for the peculiar features of the printed alloy. Topology optimization by distribution of anisotropic material is exploited to find optimal shapes in layer-by-layer manufacturing. Two-dimensional specimens are addressed along with I-beams. In the latter case it is assumed that a web plate and two flanges are printed and subsequently welded to assemble the structural component. A constrained force density method is proposed for the design of grid shells in dot-by-dot printing, formulating local enforcements to govern the magnitude of the axial force in each branch of the network. In both formulations, the arising multi-constrained problem is efficiently tackled through methods of sequential convex programming. Lightweight solutions for layer-by-layer and dot-by-dot manufacturing are found for given printing directions. Extensions of the proposed numerical tools are highlighted to endow the optimization problems with additional set of materialrelated constraints

A numerical investigation on the use of the virtual element method for topology optimization on polygonal meshes

A classical formulation of topology optimization addresses the problem of finding the best distribution of an assigned amount of isotropic material that minimizes the work of the external forces at equilibrium. In general, the discretization of the volume-constrained minimum compliance problem resorts to the adoption of four node displacement-based finite elements, coupled with element-wise density unknowns. When regular meshes made of square elements are used, well-known numerical instabilities arise, see in particular the so-called checkerboarded patterns. On the other hand, when unstructured meshes are needed to cope with geometry of any shape, additional instabilities can steer the optimizer towards local minima instead of the expected global one. Unstructured meshes approximate the strain energy of the members of the arising optimal design with an accuracy that is strictly related to the geometrical features of the discretization, thus remarkably affecting the achieved layouts. In light of the above remarks, in this contribution we consider polygonal meshes and implement the virtual element method (VEM) to solve two classes of topology optimization problems. The robustness of the adopted discretization is exploited to address problems governed by (nearly incompressible and compressible) linear elasticity and problems governed by Stokes equations. Numerical results show the capabilities of the proposed polygonal VEM-based approach with respect to more conventional discretizations

VEM and topology optimization on polygonal meshes

Topology optimization is a fertile area of research that is mainly concerned with the automatic generation of optimal layouts to solve design problems in Engineering. The classical formulation addresses the problem of finding the best distribution of an isotropic material that minimizes the work of the external loads at equilibrium, while respecting a constraint on the assigned amount of volume. This is the so-called minimum compliance formulation that can be conveniently employed to achieve stiff truss-like layout within a two-dimensional domain. A classical implementation resorts to the adoption of four node displacement-based finite elements that are coupled with an elementwise discretization of the (unknown) density field. When regular meshes made of square elements are used, well-known numerical instabilities arise, see in particular the so-called checkerboard patterns. On the other hand, when unstructured meshes are needed to cope with geometry of any shape, additional instabilities can steer the optimizer towards local minima instead of the expected global one. Unstructured meshes approximate the strain energy of truss-like members with an accuracy that is strictly related to the geometrical features of the discretization, thus remarkably affecting the achieved layouts. In this paper we will consider several benchmarks of truss design and explore the performance of the recently proposed technique known as the Virtual Element Method (VEM) in driving the topology optimization procedure. In particular, we will show how the capability of VEM of efficiently approximating elasticity equations on very general polygonal meshes can contribute to overcome the aforementioned mesh-dependent instabilities exhibited by classical finite element based discretization technique