Optimal design of the fiber-reinforcement to strengthen existing structures

An original approach is proposed to define the optimal design of any unidirectional fiber–reinforcement to improve the structural performance of existing structural elements. A problem of topology optimization is formulated, simultaneously searching for the regions to be strengthened and the optimal local fiber orientation. The maximum equivalent stress in the underlying material is minimized, for a given amount of reinforcement. The Tsai–Wu strength criterion is employed, to take into account the different strength properties of the material in tension and compression and the possible material anisotropy. Tensile stresses along the fiber direction are not allowed in the reinforcement. The resulting multi–constrained min–max problem is solved by mathematical programming. A numerical example is presented to discuss the features of the achieved optimal layouts, along with their possible application to the preliminary design of any fiber reinforcement

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

Form-finding of reticulated shells for a given plan layout with geometric constraints

A numerical tool is implemented to address the design of reticulated shells through funicular analysis. As discussed in the literature, the force density method can be conveniently implemented to cope with the equilibrium of funicular networks, using independent sets of branches in the case of grids having fixed plan projection. In this contribution, optimal networks are sought not only in terms of an independent set of force densities, but also in the vertical coordinates of the restrained nodes. Constraints are enforced on the coordinates of the nodes, to prescribe a feasible design domain, and on the geometry of the members, to control their length and inclination with respect to a given reference direction. Due to its peculiar form, the arising multiconstrained problem can be efficiently solved through techniques of sequential convex programming that were originally conceived to handle formulations of size optimization for elastic structures. Networks that are fully feasible with respect to the enforced local constraints are retrieved in a limited number of iterations, with no need to initialize the procedure with a feasible starting guess. The same algorithm applies to general networks with any type of geometry and restraints

Topology Optimization for Loads with Multiple Points of Application

The optimal design for loads with multiple points of application is herein investigated by using a formulation of displacement-constrained minimum volume topology optimization. For each one of the several points in which a moving force may be applied, a static load case is introduced, and a local enforcement is implemented to control the relevant displacement. Inspired by some recent contributions in stress-based topology optimization of large-scale structures, an Augmented Lagrangian approach, is adopted to handle efficiently the arising multi-constrained problem, in conjunction with mathematical programming. The results of some numerical simulations are shown to comment on optimal shapes for loads with multiple points of application, as compared to classical solutions for fixed loads

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

Topology optimization with graded infill accounting for loading uncertainty

The optimal design of composite structures made of a solid phase and a given fraction of graded infill is addressed, using homogenization-based topology optimization and accounting for uncertainty in loading amplitude. A two-phase material law with void is implemented to control the amount of graded infill to be distributed, along with its admissible density range. Numerical homogenization is used to derive the macroscopic elastic properties of an isotropic and two orthotropic infills that are commonly used in additive manufacturing. A minimum weight problem is endowed with a set of deterministic displacement constraints that are equivalent to stochastic displacement enforcements in case of normal distributions of the amplitude of the applied forces. Sequential convex programming is adopted to solve the arising multi-constrained problem. Numerical simulations are performed to assess the proposed algorithm and point out peculiar features of the achieved optimal solutions with respect to layouts found in case of deterministic loads. When a fraction of graded infill is prescribed, coated structures are retrieved, whose shape may be remarkably affected by the selected type of lattice