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This paper aims to propose a new boundary condition and a web-spline basis of finite element space approximation to remedy the problems of constraints due to homogeneous and non-homogeneous; Dirichlet boundary conditions. This paper considered the two-dimensional linear elasticity equation of Navier–Lamé with the condition CAB. The latter allows to have a total insertion of the essential boundary condition in the linear system obtained; without using a numerical method as Lagrange multiplier. This study have developed mixed finite element; method using the B-splines Web-spline space. These provide an exact implementation of the homogeneous; Dirichlet boundary conditions, which removes the constraints caused by the standard; conditions. This paper showed the existence and the uniqueness of the weak solution, as well as the convergence of the numerical solution for the quadratic case are proved. The weighted extended B-spline; approach have become a much more workmanlike solution.

In this paper, this study used the implementation of weighted finite element methods to solve the Navier–Lamé system with a new boundary condition CA, B (Koubaiti et al., 2020), that generalises the well-known basis, especially the Dirichlet and the Neumann conditions. The novel proposed boundary condition permits to use a single Matlab code, which summarises all kind of boundary conditions encountered in the system. By using this model is possible to save time and programming recourses while reap several programs in a single directory.

The results have shown that the Web-spline-based quadratic-linear finite elements satisfy the inf–sup condition, which is necessary for existence and uniqueness of the solution. It was demonstrated by the existence of the discrete solution. A full convergence was established using the numerical solution for the quadratic case. Due to limited regularity of the Navier–Lamé problem, it will not change by increasing the degree of the Web-spline. The computed relative errors and their rates indicate that they are of order 1/H. Thus, it was provided their theoretical validity for the numerical solution stability. The advantage of this problem that uses the CA, B boundary condition is associated to reduce Matlab programming complexity.

The mixed finite element method is a robust technique to solve difficult challenges from engineering and physical sciences using the partial differential equations. Some of the important applications include structural mechanics, fluid flow, thermodynamics and electromagnetic fields (Zienkiewicz and Taylor, 2000) that are mainly based on the approximation of Lagrange. However, this type of approximation has experienced a great restriction in the level of domain modelling, especially in the case of complicated boundaries such as that in the form of curvilinear graphs. Recently, the research community tried to develop a new way of approximation based on the so-called B-spline that seems to have superior results in solving the engineering problems.

The purpose of this study is to explore the applications of 3D printing in space sectors. The authors have highlighted the potential research gap that can be explored in the current field of study. Three-dimensional (3D) printing is an additive manufacturing technique that uses metallic powder, ceramic or polymers to build simple/complex parts. The parts produced possess good strength, low weight and excellent mechanical properties and are cost-effective. Therefore, efforts have been made to make the adoption of 3D printing successful in space so that complex parts can be manufactured in space. This saves a considerable amount of both time and carrying cost. Thereof the challenges and opportunities that the space sector holds for additive manufacturing is worth reviewing to provide a better insight into further developments and prospects for this technology.

The potentiality of 3D printing for the manufacturing of various components under space conditions has been explained. Here, the authors have reviewed the details of manufactured parts used for zero-gravity missions, subjected to onboard international space station conditions and with those manufactured on earth. Followed by the major opportunities in 3D printing in space which include component repair, material characterization, process improvement and process development along with the new designs. The challenges like space conditions, availability of power in space, the infrastructure requirements and the quality control or testing of the items that are being built in space are explained along with their possible mitigation strategies.

These components are well comparable with those prepared on earth which enables a massive cost saving. Other than the onboard manufacturing process, numerous other components as well as a complete robot/satellite for outer space applications were manufactured by additive manufacturing. Moreover, these components can be recycled onboard to produce feedstock for the next materials. The parts produced in space are bought back and compared with those built on earth. There is a difference in their nature, i.e. the flight specimen showed a brittle nature, and the ground specimen showed a denser nature.

This review discusses the advancements of 3D printing in space and provides numerous examples of the applications of 3D printing in space and space applications. This paper is solely dedicated to 3D printing in space. It provides a breakthrough in the literature as a limited amount of literature is available on this topic. This paper aims at highlighting all the challenges that additive manufacturing faces in the space sector and also the future opportunities that await development.