Implementation of different types of meshfree technique in computational solid mechanics: a comprehensive review across nano, micro, and macro scales

This work is considered as the first comprehensive review, that covers all types of meshfree method including the traditional or developed meshless techniques that have been implemented for the purpose of investigating static analysis (bending, stability) besides dynamic analysis (free vibration, force vibration and other types of dynamic behaviors) of linear and nonlinear mechanical system. The secondary methods utilized together with the meshless methods are also highlighted such as; Hamilton’s principle, first-order shear deformation theory, high-order shear deformation theory, Monte Carlo, local/nonlocal theories and others. Also, some computational mechanics approaches are briefly addressed. The basic fundamental equations of meshfree methods and the error analysis are presented. Various types of schematics and structure size are discussed. Else, the implementation of composite material in solid mechanics are concisely highlighted. As a key finding, in each unique schematic in specific scale, various implemented parameters like boundary conditions, thickness to length ratio (t/l), as well as the aspect ratio have different impacts on the mechanical performance in both static and dynamic analysis. Additionally, as each meshfree method is considered unique by itself and has its own developed mathematical model, each method has different application and numerical problems to solve. Galerkin, reproducing kernel particle method, moving least square are the most common meshfree. Based on the literature, many studies mainly show interest in investigating the piezoelectric and diverse distribution of carbon nanotubes, and some in fictional graded material in different structures. This review is recommended for researchers interested in solid mechanics analysis at various scales using meshfree techniques.