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A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities.

A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Belytschko error estimation procedure are used in the FE and meshless regions of the problem domain, respectively. The message passing interface library and open-source software packages, METIS and MUltifrontal Massively Parallel Solver are used for the high performance computation.

Numerical examples are given to demonstrate the correct implementation and performance of the parallel algorithms. The agreement between the numerical and analytical results in the case of linear elastic example is excellent. For the nonlinear problems load-displacement curve are compared with the reference FEM and found in a very good agreement. As compared to the FEM, no volumetric locking was observed in the case of meshless method. Furthermore, it is shown that increasing the number of processors up to a given number improve the performance of parallel algorithms in term of simulation time, speedup and efficiency.

Problems involving both material and geometrical nonlinearities are of practical importance in many engineering applications, e.g. geomechanics, metal forming and biomechanics. A family of parallel algorithms has been developed in this paper for these problems using adaptively coupled finite element, meshless method (based on maximum entropy basis functions) for distributed memory computer architectures.

In this paper, a modified meshless method, as one of the numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to solving time-domain wave equation. The paper aims to discuss these issues.

In space domain, the fields at the collocation points are expanded into a series of new Shepard's functions which have been suggested recently and are treated with a meshless method procedure. For time discretization of the second-order time-derivative, two finite-difference schemes, i.e. backward difference and Newmark-β techniques, are proposed.

Both schemes are implicit and always stable and have unconditional stability with different orders of accuracy and numerical dispersion. The unconditional stability of the proposed methods is analytically proven and numerically verified. Moreover, two numerical examples for electromagnetic field computation are also presented to investigate characteristics of the proposed methods.

The paper presents two unconditionally stable schemes for meshless methods in time-domain electromagnetic problems.

The purpose of this paper is to present a micromechanical model based on a new truly local meshless method for analysis of heat transfer in composite materials.

The presented meshless method is based on the integral form of energy equation in the sub‐particles in the material. In the presented meshless method due to elimination of domain integration the computational efforts are decreased substantially.

Numerical results are presented for temperature distribution, heat flux and thermal conductivity. Numerical results show that the presented meshless method is simple, effective, accurate and less costly method in micromechanical modeling of heat conduction in heterogeneous materials.

A small area of the composite system called representative volume element is considered as the solution domain. The fully bonded fiber‐matrix interface is considered and contact thermal resistant is neglected from the fiber matrix interface and so the continuity of temperature and reciprocity of heat flux is satisfied in the fiber‐matrix interface.

For the first time a new truly local meshless method based on the integral form of energy equation for the sub‐particles in the materials is presented for analysis of heat transfer in composite materials.

The study aims to present a new meshless method based on the Taylor series expansion. The compact supported radial basis functions (CSRBFs) are very attractive, can be considered as a numerical tool for the engineering problems and used to obtain the trial solution and its derivatives without differentiating the basis functions for a meshless method. A meshless based on the CSRBF and Taylor series method has been developed for the solutions of engineering problems.

This paper is devoted to present a truly meshless method which is called a radial basis Taylor series method (RBTSM) based on the CSRBFs and Taylor series expansion (TSE). The basis function and its derivatives are obtained without differentiating CSRBFs.

The RBTSM does not involve differentiation of the approximated function. This property allows us to use a wide range of CSRBF and weight functions including the constant one. By using a different number of terms in the TSE, the global convergence properties of the RBTSM can be improved. The global convergence properties are satisfied by the RBTSM. The computed results based on the RBTSM shows excellent agreement with results given in the open literature. The RBTSM can provide satisfactory results even with the problem domains which have curved boundaries and irregularly distributed nodes.

The CSRBFs have been widely used for the construction of the basic function in the meshless methods. However, the derivative of the basis function is obtained with the differentiation of the CSRBF. In the RBTSM, the derivatives of the basis function are obtained by using the TSE without differentiating the CSRBF.

The purpose of this paper is to investigate an active flow control technique called Shock Control Bump (SCB) for drag reduction using evolutionary algorithms.

A hierarchical genetic algorithm (HGA) consisting of multi‐fidelity models in three hierarchical topological layers is explored to speed up the design optimization process. The top layer consists of a single sub‐population operating on a precise model. On the middle layer, two sub‐populations operate on a model of intermediate accuracy. The bottom layer, consisting of four sub‐populations (two for each middle layer populations), operates on a coarse model. It is well‐known that genetic algorithms (GAs) are different from deterministic optimization tools in mimicking biological evolution based on Darwinian principle. In HGAs process, each population is handled by GA and the best genetic information obtained in the second or third layer migrates to the first or second layer for refinement.

The method was validated on a real life optimization problem consisting of two‐dimensional SCB design optimization installed on a natural laminar flow airfoil (RAE5243). Numerical results show that HGA is more efficient and achieves more drag reduction compared to a single population based GA.

Although the idea of HGA approach is not new, the novelty of this paper is to combine it with mesh/meshless methods and multi‐fidelity flow analyzers. To take the full benefit of using hierarchical topology, the following conditions are implemented: the first layer uses a precise meshless Euler solver with fine cloud of points, the second layer uses a hybrid mesh/meshless Euler solver with intermediate mesh/clouds of points, the third layer uses a less fine mesh with Euler solver to explore efficiently the search space with large mutation span.

The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF) method, based on classical continuum mechanics, to solve planar problems.

The coupling has been achieved in a completely meshless scheme. The domain is divided in three zones: one in which only Peridynamics is applied, one in which only the meshless method is applied and a transition zone where a gradual transition between the two approaches takes place.

The new coupling technique generates overall grids that are not affected by ghost forces. Moreover, the use of the meshless approach can be limited to a narrow boundary region of the domain, and in this way, it can be used to remove the “surface effect” from the Peridynamic solution applied to all internal points.

The current study paves the road for future studies on dynamic and static crack propagation problems.

Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless techniques are simple and well understood, an effective meshless method is very difficult to develop. The efficiency depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of imposing the boundary conditions. These issues in the context of the method of finite spheres are discussed.

The purpose of this paper is to present a new approach of meshless local B-spline based finite difference (FD) method for solving two dimensional transient heat conduction problems.

In the present method, any governing equations are discretized by B-spline approximation which is implemented in the spirit of FD technique using a local B-spline collocation scheme. The key aspect of the method is that any derivative is stated as neighbouring nodal values based on B-spline interpolants. The set of neighbouring nodes are allowed to be randomly distributed thus enhanced flexibility in the numerical simulation can be obtained. The method requires no mesh connectivity at all for either field variable approximation or integration. Time integration is performed by using the Crank-Nicolson implicit time stepping technique.

Several heat conduction problems in complex domains which represent for extended surfaces in industrial applications are examined to demonstrate the effectiveness of the present approach. Comparison of the obtained results with solutions from other numerical method available in literature is given. Excellent agreement with reference numerical method has been found.

The method is presented for 2D problems. Nevertheless, it would be also applicable for 3D problems.

A transient two dimensional heat conduction in complex domains which represent for extended surfaces in industrial applications is presented.

The presented new meshless local method is simple and accurate, while it is also suitable for analysis in domains of arbitrary geometries.

Fused Filament Fabrication (FFF) is an extrusion-based manufacturing process using fused thermoplastics. Despite its low cost, the FFF is not extensively used in high-value industrial sectors mainly due to parts' anisotropy (related to the deposition strategy) and residual stresses (caused by successive heating cycles). Thus, this study aims to investigate the process improvement and the optimization of the printed parts.

In this work, a meshless technique – the Radial Point Interpolation Method (RPIM) – is used to numerically simulate the viscoplastic extrusion process – the initial phase of the FFF. Unlike the FEM, in meshless methods, there is no pre-established relationship between the nodes so the nodal mesh will not face mesh distortions and the discretization can easily be modified by adding or removing nodes from the initial nodal mesh. The accuracy of the obtained results highlights the importance of using meshless techniques in this field.

Meshless methods show particular relevance in this topic since the nodes can be distributed to match the layer-by-layer growing condition of the printing process.

Using the flow formulation combined with the heat transfer formulation presented here for the first time within an in-house RPIM code, an algorithm is proposed, implemented and validated for benchmark examples.

The purpose of the present work is to develop the combination of the radial point interpolation method (RPIM) with a bi-directional evolutionary structural optimization (BESO) algorithm and extend it to the analysis of benchmark examples and automotive industry applications.

A BESO algorithm capable of detecting variations in the stress level of the structure, and thus respond to those changes by reinforcing the solid material, is developed. A meshless method, the RPIM, is used to iteratively obtain the stress field. The obtained optimal topologies are then recreated and numerically analyzed to validate its proficiency.

The proposed algorithm is capable to achieve accurate benchmark material distributions. Implementation of the BESO algorithm combined with the RPIM allows developing innovative lightweight automotive structures with increased performance.

Computational cost of the topology optimization analysis is constrained by the nodal density discretizing the problem domain. Topology optimization solutions are usually complex, whereby they must be fabricated by additive manufacturing techniques and experimentally validated.

In automotive industry, fuel consumption, carbon emissions and vehicle performance is influenced by structure weight. Therefore, implementation of accurate topology optimization algorithms to design lightweight (cost-efficient) components will be an asset in industry.

Meshless methods applications in topology optimization are not as widespread as the finite element method (FEM). Therefore, this work enhances the state-of-the-art of meshless methods and demonstrates the suitability of the RPIM to solve topology optimization problems. Innovative lightweight automotive structures are developed using the proposed methodology.