Fuel-Optimal Ascent Trajectory Problem for Launch Vehicle via Theory of Functional Connections

In this study, we develop a method based on the Theory of Functional Connections (TFC) to solve the fuel-optimal problem in the ascending phase of the launch vehicle. The problem is first transformed into a nonlinear two-point boundary value problem (TPBVP) using the indirect method. Then, using the function interpolation technique called the TFC, the problem’s constraints are analytically embedded into a functional, and the TPBVP is transformed into an unconstrained optimization problem that includes orthogonal polynomials with unknown coefficients. This process effectively reduces the search space of the solution because the original constrained problem transformed into an unconstrained problem, and thus, the unknown coefficients of the unconstrained expression can be solved using simple numerical methods. Finally, the proposed algorithm is validated by comparing to a general nonlinear optimal control software GPOPS-II and the traditional indirect numerical method. The results demonstrated that the proposed algorithm is robust to poor initial values, and solutions can be solved in less than 300 ms within the MATLAB implementation. Consequently, the proposed method has the potential to generate optimal trajectories on-board in real time.

Floating-bending tensile-integrity structures

This is a conceptual work about the form-finding of a hybrid tensegrity structure. The structure was obtained from the combination of arch-supported membrane systems and diamond-type tensegrity systems. By combining these two types of structures, the resulting system features the “tensile-integrity” property of cables and membrane together with what we call “floating-bending” of the arches, a term which is intended to recall the words “floating-compression” introduced by Kenneth Snelson, the father of tensegrities. Two approaches in the form-finding calculations were followed, the Matlab implementation of a simple model comprising standard constant-stress membrane/cable elements together with the so-called stick-and-spring elements for the arches, and the analysis with the commercial software WinTess, used in conjunction with Rhino and Grasshopper. The case study of a T3 floating-bending tensile-integrity structure was explored, a structure that features a much larger enclosed volume in comparison to conventional tensegrity prisms. The structural design of an outdoor pavilion of 6 m in height was carried out considering ultimate and service limit states. This study shows that floating-bending structures are feasible, opening the way to the introduction of suitable analysis and optimization procedures for this type of structures.

ArchLab: a MATLAB tool for the Thrust Line Analysis of masonry arches

According to Heyman’s safe theorem of the limit analysis of masonry structures, the safety of masonry arches can be verified by finding at least one line of thrust entirely laying within the masonry and in equilibrium with external loads. If such a solution does exist, two extreme configurations of the thrust line can be determined, respectively referred to as solutions of minimum and maximum thrust. In this paper it is presented a numerical procedure for determining both these solutions with reference to masonry arches of general shape, subjected to both vertical and horizontal loads. The algorithm takes advantage of a simplification of the equations underlying the Thrust Network Analysis. Actually, for the case of planar lines of thrust, the horizontal components of the reference thrusts can be computed in closed form at each iteration and for any arbitrary loading condition. The heights of the points of the thrust line are then computed by solving a constrained linear optimization problem by means of the Dual-Simplex algorithm. The MATLAB implementation of presented algorithm is described in detail and made freely available to interested users (https://bit.ly/3krlVxH). Two numerical examples regarding a pointed and a lowered circular arch are presented in order to show the performance of the method.