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This paper sets propelling a more current strategy for mechanical shape optimization by joining a coupled finite element (FE) method–meshfree method (MM) with swarm intelligence (SI)-based stochastic 'zero-order' search procedure. The arranged gathering massively fits as a structural shape optimization since MM is utilized here for structural examination shape analysis and to avoid a remeshing in view of fundamental mesh modification if there should be an occurrence of tremendous shape varieties, discontinuous secondary field variables across element boundaries, etc. while using FE. This is same as FE strategy that helps in beating the weaknesses of MM like high computational exertion and simplicity of forcing essential boundary conditions (EBCs). Populace-based stochastic optimization strategy, e.g., PSO abrogates computational burden, multifaceted nature and blunders aligned with structure affectability assessment Right now, plan limit portrayal Akima spline introduction has been considered on account of its improved persistence and smoothness over cubic spline. The convenience of present strategy, results got with current technique is contrasted and different strategies for past writing. The adequacy, legitimacy and execution of the present procedure are built up through mathematical instances of cantilever beam and fixed–fixed bar geometry for shape optimization with conduct limitations on displacement. For both these issues, h-refinement for opening issue geometry has been examined and furthermore impact of various design variables fit as a shape optimization has likewise been researched. [ABSTRACT FROM AUTHOR]

In many engineering problems, the meshfree methods (MMs) have been dynamically projected and increasingly advanced in order to overwhelm some hitches in the predictable numerical methods. Over the past three decades in many different application area, MMs have found their way ranging from solid mechanics analysis, fluid problems, vibration analysis, heat transfer and optimization to numerical solutions of all kinds of (partial) differential equations. As every technique has shortcomings, the meshfree method also has drawbacks like higher computational cost and imposition of boundary condition which can be overruled by coupling it with the finite element method (FEM). In the past two decades, coupled MMs and FEM have appeared into a new session of computational methods with significant achievement. In addition, a noteworthy amount of growth has been made in addressing the major deficiencies that were present in the conventional methods and MMs at the premature phases. The objective of the present work is to provide a comprehensive review of various coupling techniques used for interface elements of MMs and FEM and general discussion on shape function formulation of FE and element free Galerkin method (EFGM). Key contribution of coupling techniques for coupled EFGM and FEM to structure mechanics application as primary concern. [ABSTRACT FROM AUTHOR]