Meshfree Radial Point Interpolation Method Research Articles

Nonlinear dynamic analysis of aircraft CFRP sandwich wings under explosive blast loading: Introducing SVM-DNN algorithm to predict dynamical information

The aircraft wings are a crucial component, particularly during mechanical shock excitation. Thus, for the first time, an inventive adaptable model to simulate the nonlinear dynamics of the wings under explosive blast loading at the moment of the collision is described in this article. It is crucial to increase the structure's stability because of explosive blast loading. The mentioned structure is made of two composite face sheets and a carbon fiber-reinforced polymer (CFRP). Functionally graded (FG) graphene origami (GOri)-enabled auxetic metallic metamaterial (GOEAM) is introduced to improve the stability of this kind of applicable structure, especially in air maneuvers. The analysis is conducted utilizing Reddy's third-order shear deformation of Reddy theory (TSDRT), incorporating Hamilton's principle and Von Kármán nonlinear geometric assumptions. The governing and boundary equations are accurately computed at the domain and boundary edges of the doubly curved structure. The coupled mesh-free radial point interpolation method (MRPIM) and Newton-Raphson method are applied for numerically simulating the current doubly curved structure by employing Newmark's temporal integration method with a constant-average acceleration approach. The present findings are cross-checked against the machine learning method and open-source results from the literature. Based on physical data, machine learning integrates supervised machine learning to predict the nonlinear vibration of the system. In this case, nonlinear transient bending properties are found using hybrid machine learning methods and solutions. The findings demonstrate the significance of GOEAM for nonlinear vibrations of the composite system. The current study's conclusions could be used as a benchmark and useful recommendations for future structural design techniques with enhanced features.

Dynamic analysis of sandwich conical shell with magneto/electro rheological core using a truly meshfree radial point interpolation method

Dynamic analysis of sandwich conical shell with magneto/electro rheological core using a truly meshfree radial point interpolation method

Transient analyses of underwater acoustic propagation with the modified meshfree radial point interpolation method and newmark time integration techniques

Underwater acoustic propagation plays a very important role in underwater communication and ocean engineering field. The radial point interpolation method (RPIM) is an effective numerical approach to solve underwater acoustic propagations though considerable numerical errors can always be caused due to the discontinuously differentiable nodal interpolation function in one integration cell. The origin of this numerical error primarily comes from the mismatch between the background integration cell and the nodal interpolation function support. To address this issue, a modified meshfree RPIM is developed in this work for transient analyses of underwater acoustic propagations. In the proposed modified RPIM, the construction of the interpolation function supports are dependent on the integration cells. In consequence, in one background cell all the quadrature points share one mutual support domain and the continuously differentiable interpolation functions can be obtained. Therefore, the numerical integration errors can be evidently decreased and the related numerical dispersion effects in wave analysis can be largely suppressed. Owing to the adequately small spatial dispersion errors from the proposed modified RPIM, it is observed that the modified RPIM with the Newmark time domain discretization scheme can monotonically improve the solution precision by directly reducing the temporal discretization interval. This property makes the modified RPIM clearly outperform the original RPIM and is especially suitable for handling very complex underwater acoustic propagations.

The efficient data-driven solution to estimate the nonlinear bending of sandwich doubly curved panel subjected to transient loading

This paper investigates nonlinear transient bending characteristics of sandwich doubly curved panels under transient loading which is extensively used in aerospace structures. Due to the lack of a dataset for the nonlinear transient bending of the sandwich doubly curved panel for the data-driven solution, mathematical modeling is used. The sandwich doubly curved panel is made of two graphene nanoplatelets (GPLs) reinforced face sheets, and a polymer core. In the mathematical modeling section, the effective Young's modulus is obtained via modified Halpin-Tsai methodology, and the role of the mixture is used to estimate other material properties of the composite face sheets. The presented structure is analyzed using Reddy's third-order shear deformation theory (RTSDT), which incorporates von Kármán nonlinear geometric assumptions and Hamilton's principle. The governing equations and associated boundary conditions are derived accurately by imposing shear stress-free conditions on the upper and lower surfaces of the panel. The meshfree radial point interpolation method (RPIM) with interpolation functions is utilized to determine the unknown degrees of freedom to numerically simulate the mid-plane of the sandwich doubly-curved panel. The Newton-Raphson approach is used to solve the nonlinear ordinary differential using the constant-average acceleration strategy from Newmark's time integration method. After obtaining the dataset, the data is collected, and using an efficient data-driven approach, the results are tested, validated, and trained. In future studies, the presented efficient data-driven approach can be used with low computational cost to simulate nonlinear transient bending characteristics of sandwich doubly curved panels under transient loading for related aerospace industries.

Time-domain acoustic wave propagations in multi-fluids using a weak-form meshfree method

In this work, we focus on the derivation of the weak-form for meshfree methods in analyzing the time-domain acoustic wave propagation in multi-fluids. Due to the employment of meshfree shape functions not restricted to a local background cell, the continuity condition for acoustic particle velocity cannot be spontaneously satisfied, leading to inaccurate simulations of acoustic wave upon the interface. Thus, the penalty function method is utilized here in the weak-form for meshfree methods in order to cure this discontinuity issue without introducing any addition degrees of freedom. By conducting a number of numerical analyses, the numerical results obtained from a radial point interpolation meshfree method are in accord with the analytical solutions and the numerical results of bilinear and quadratic finite elements, validating the effectiveness of the weak-form derived for meshfree methods. Moreover, the numerical accuracy of the used meshfree method can surpass those of bilinear and quadratic finite elements when the same sets of nodes are employed, especially for relatively high frequencies.

Real-time temperature field reconstruction using a few measurement points and RPIM-AGQ6 interpolation

In thermal management systems, temperature field monitoring is vital for the structural safety of electronic equipment. However, there are practical challenges when it comes to installing temperature sensors on some monitoring points directly. To solve this problem, a novel temperature field reconstruction method is proposed. This strategy offers the advantage of using only a limited number of discrete values to predict temperature fields across an entire plane. Initially, the approach constructs a composite interpolation function, named RPIM-AGQ6, by coupling the mesh-free radial point interpolation method (RPIM) with the quadrilateral area coordinate method (AGQ6) The temperature field is discretized and represented as the product of the nodal temperatures and the RPIM-AGQ6. Next, ill-posed equations are established and solved using Bayesian Multivariate Linear Regression (BMLR) to obtain the temperature in the key points. Subsequently, a novel optimization strategy is proposed to achieve the cooperative optimization of the number of sensors and reconstruction accuracy. Finally, the simulated calculation and experimental tests are used to demonstrate the effectiveness and accuracy of the proposed approach. The results show that the proposed methodology can accurately reconstruct the plane temperature field of plate structure with one and two hot sources and the relative percentage error is within 2.6 %. Therefore, it can be utilized as an effective tool to real-time monitor structural surface temperature.

A local meshfree radial point interpolation method for Berger equation arising in modelling of thin plates

In this study, two-dimensional (2D) Berger equation arising in deflection of thin plates is solved numerically. A local meshfree collocation technique based on radial point interpolation is developed for the Berger equation. As radial basis function thin plate splines are used to avoid selecting optimal shape parameter. The method is used to solve both linear and non-linear Berger equation on regular and irregular geometries. Obtained results during numerical simulations, are compared with different methods exist in literatrue such as method of fundamental solutions, local Kansa’s method and Pascal polynomial based meshless method. The comparisons affirm the accuracy and reliability of the suggested method.

Investigating nonlinear moving load responses of FG-GPLRC skew plates using meshfree radial point interpolation method

Investigating nonlinear moving load responses of FG-GPLRC skew plates using meshfree radial point interpolation method

The Meshfree Radial Point Interpolation Method (RPIM) for Wave Propagation Dynamics in Non-Homogeneous Media

This work presents a novel simulation approach to couple the meshfree radial point interpolation method (RPIM) with the implicit direct time integration method for the transient analysis of wave propagation dynamics in non-homogeneous media. In this approach, the RPIM is adopted for the discretization of the overall space domain, while the discretization of the time domain is completed by employing the efficient Bathe time stepping scheme. The dispersion analysis demonstrates that, in wave analysis, the amount of numerical dispersion error resulting from the discretization in the space domain can be suppressed at a very low level when the employed nodal support domain of the interpolation function is adequately large. Meanwhile, it is also mathematically shown that the amount of numerical error resulting from the time domain discretization is actually a monotonically decreasing function of the non-dimensional time domain discretization interval. Consequently, the present simulation approach is capable of effectively handling the transient analysis of wave propagation dynamics in non-homogeneous media, and the disparate waves with different speeds can be solved concurrently with very high computation accuracy. This numerical feature makes the present simulation approach more suitable for complicated wave analysis than the traditional finite element approach because the waves with disparate speeds always cannot be concurrently solved accurately. Several numerical tests are given to check the performance of the present simulation approach for the analysis of wave propagation dynamics in non-homogeneous media.

Abstract 13581: Prognostic Value of Left Ventricular Global Longitudinal Strain for Early Prediction of Cancer Therapy-Related Cardiac Dysfunction

Introduction: This prospective study aimed to determine if MRI-imaging and Artificial Intelligence (AI)-based computation of global longitudinal strain (GLS) in the left ventricle (LV) is an early predictor of cancer therapy-related cardiac dysfunction (CTRCD) in breast cancer patients. Hypothesis: To show with risk analysis that GLS is an independent prognosticator of CTRCD when compared to LV ejection fraction (LVEF) with the patient cohort administered antineoplastic chemotherapy treatment. Methods: Motion-encoded data with Displacement Encoding with Stimulated Echoes (DENSE) MRI were acquired on 32 breast cancer patients at baseline and 3- and 6-months follow-ups after chemotherapy. Automated image segmentation for chamber quantification and phase-unwrapping in the LV occurred with two DeepLabV3+ fully convolutional networks (FCNs), and 3D strains computed with the meshfree Radial Point Interpolation Method. CTRCD (including adverse cardiac events and cardiotoxicity) risk analyses with the measured clinical, chamber quantification, and strain parameters were conducted with univariable and bivariable Cox proportional hazard (PH) regressions. Results: GLS worsened from baseline to the 3- and 6-months follow-ups (-19.1 ± 2.1% vs. -16.0 ± 3.1% vs. -16.1 ± 2.9%, P<0.001) (Fig. 1). With univariable Cox regression, the 3-months follow-up GLS was independently associated as an agonist (hazard ratio [HR]-per-SD: 2.1; 95% CI: 1.4-3.1, P<0.001) and LVEF as protector (HR-per-SD: 0.8; 95% CI: 0.7-0.9, P<0.001) for CTRCD occurrence. In bivariable regression, GLS (HR-per-SD: 2.0; 95% CI: 1.2-3.4, P=0.01) was an independent predictor of CTRCD regardless of LVEF (HR-per-SD: 1.0; 95% CI: 0.9-1.2, P=0.9) as covariate. Conclusions: The end-point risk analyses show that LV GLS is an early CTRCD predictor independent of LVEF in breast cancer patients treated with antineoplastic chemotherapy. GLS should be a standard metric for the clinical diagnosis of CTRCD.

Interlayer shearing and bending performances of ballastless track plates based on high-order shear deformation theory (HSDT) for laminated structures

Based on higher-order shear deformation theory (HSDT), the bending of China Railway Track System type II (CRTS-II) track laminated plates on elastic foundations and interlayer shearing performances are analyzed by meshfree radial point interpolation method (RPIM), which has the properties of the Kronecker function and discretizes the governing equations derived from HSDT. To verify the applicability of the model, the geometric configuration and key parameters of the CRTS-II slab ballastless track structure are analyzed, and the interlaminar slip model of the track structure is derived as a benchmark solution when calculating the track structure using HSDT-RPIM. The accuracy of the derivation is verified by comparing the HSDT-RPIM model with a double-layer slab model considering bidirectional interlayer slip. Then, the effect of resistant slip coefficient on the bending deformation of the track structure was analyzed using the bidirectional interlaminar slip model. The effect of elastic foundation coefficient on the bending of the track structure and the interlayer slip of the track structure (track slab – base slab) was analyzed. Finally, the effects of boundary conditions and elastic foundation coefficients on the interlaminar stresses of the track structure are investigated using HSDT-RPIM, and some interlaminar damages of the track structure are explained.

A novel meshfree radial point interpolation method with discrete shear gap for nonlinear static analysis of functionally graded plates

A novel meshfree radial point interpolation method with discrete shear gap for nonlinear static analysis of functionally graded plates

A meshfree-based topology optimization approach without calculation of sensitivity

This paper presents a novel topology optimization approach without calculation of sensitivity for the minimum compliance problems, based on the meshfree Radial Point Interpolation Method (RPIM). Relying on the algorithm of Proportional Topology Optimization (PTO), material is distributed using only information of the objective function (which is the elastic strain energy). Material properties are interpolated by the well-known Solid Isotropic Material with Penalization (SIMP) technique; however the pseudo density (design variables) are not defined on the element center as usually encountered in finite element-based approaches, but on integration points. Since no element exists in meshfree analysis, this would be a natural choice. More importantly, the number of integration points is in general larger than that of elements or that of nodes, resulting in higher resolution of the density field. The feasibility and efficiency of the proposed approach are demonstrated and discussed via several numerical examples.

Airy-based static limit analysis of structures using stabilized radial point interpolation method

This paper presents a novel formulation for static limit analysis of structures, for which the Airy stress function is approximated using stabilized Radial Point Interpolation Mesh-free method (RPIM). The stress field is determined as second-order derivatives of the Airy function, and the equilibrium equations are automatically satisfied a priori. The so-called Stabilized Conforming Nodal Integration (SCNI) is employed to ensure a present method is truly a mesh-free approach, meaning that all constraints in problems are only enforced at nodes. With the use of the Airy function, SCNI, and Second-Order Cone Programming (SOCP), the size of the resulting problem is kept to be minimum. Several benchmark problems having arbitrary geometries and boundary conditions are investigated. The obtained numerical solutions are compared with those available in other studies to perform the computational aspect of the proposed method.

Coupling of NURBS and Meshfree RPIM for plane stress of web with openings

This study presents a novel approach for the coupling of the non-uniform rational B-spline (NURBS) with the radial basis functions (RBF) under the framework of the meshfree radial point interpolation method (RPIM). In this method, denoted as N-RPIM, the NURBS basis functions are employed to model the geometry of the problem domain exactly, whilst the RPIM is used for field variables interpolation. The formulation is applied to the web of a cellular beam under plane stress condition to highlight the advantages. The results show that the method works efficiently, and provides favourable performance against FEM. The solution of the former converges faster, thus highlighting the potential of N-RPIM for future development.

Modeling fracture in viscoelastic materials using a modified incremental meshfree RPIM and DIC technique

In the present work, fracture mechanics of linear viscoelastic materials is investigated numerically and experimentally. Herein, an effective and accurate meshfree method is developed to analyze fracture mechanics in viscoelastic problems. To this end, an incremental approach with higher-order finite difference (FD) schemes for analysis of viscoelastic materials in the time domain, along with an improved meshfree method based on the global weak formulation, i.e. the radial point interpolation method (RPIM), is employed. An accurate and efficient integration approach with minimum computational cost, i.e. the background decomposition method (BDM), is also used to compute the domain integrals. To evaluate the accuracy and efficiency of the proposed numerical method, first, two example problems are provided and the robustness of the presented method is assessed. Then, a non-contact full-field optical method, i.e. the digital image correlation technique, is utilized to investigate the viscoelastic fields of a polymer, polymethyl-methacrylate (PMMA), during crack propagation in mode I. Also, in order to properly model the fracture behavior of this material by the meshfree RPIM, the mechanical properties of the PMMA, including the Prony viscoelastic parameters, are obtained by an ASTM test method. Moreover, the obtained results from the DIC test and also the load-displacement curve of the cracked specimen are compared with the results of the proposed meshfree RPIM and a very close agreement is observed.

An effective crack identification method in viscoelastic media using an inverse meshfree method

In the present study, a numerical approach is proposed for identification of straight cracks in two-dimensional linear viscoelastic media. The identification procedure is based on the wave propagation in cracked viscoelastic media. The forward wave propagation problem in viscoelastic media is solved using the meshfree radial point interpolation method (RPIM), which allows the crack boundary to be easily modelled at any part of the domain. In the meshfree approach, the crack position can be changed freely during the iterations of the identification procedure. A modified higher-order incremental method is implemented for modelling dynamic behaviour of linear viscoelastic materials. Also, the integration points are determined using the background decomposition method (BDM). Firstly, the wave propagation behaviour in viscoelastic media is studied, and the effect of crack on wave propagation is investigated. Then, the inverse identification task is formulated as a nonlinear optimization problem to determine the unknown crack parameters. The optimization problem is solved by a gradient-based inverse method. Several numerical tests are simulated with different number of sensors, crack size, and various initial guesses, to demonstrate the capability of the proposed techniques in obtaining accurate results. Also, it is shown that the proposed method is robust to tackle reasonable levels of measurement error. In addition, the method is investigated for different placement patterns for several sensors and the effect of number of sensors on identification of the crack is studied.

A practical meshfree inverse method for identification of thermo-mechanical fracture load of a body by examining the crack path in the body

An inverse meshfree approach is presented for thermo-mechanical load identification of a fractured body. To this end, the crack propagation path is used as the input of the inverse analysis. This study can be used for finding the thermo-mechanical loads that have led to the fracture of a body, and is applicable to situations where the direct measurement of the boundary loadings on some part of a body is not possible. This highly ill-posed problem is solved using the meshfree radial point interpolation method (RPIM) with a global optimization approach. The inspected crack path is compared to the one obtained numerically and their difference is set as a cost function. By finding the minimum of this cost function, the actual loading conditions that have led to the fracture of the body is obtained. The density clustering method is used as the global optimization method in which the damped Gauss-Newton technique is used as the local search algorithm. To demonstrate the performance of the presented meshfree inverse approach, two examples are provided.

Dynamic response and optimization of functionally graded porous nanocomposite cylinders using a meshfree method

AbstractA new class of advanced ultralight composite materials has recently emerged through the use porous polymer matrix reinforced by carbon nanotubes. In this article, the dynamic response of functionally graded porous polymeric cylinders, reinforced by randomly oriented single‐walled carbon nanotubes, using a meshfree method is studied. Three different porosity distribution patterns are investigated: symmetric distribution (SYD), unsymmetric distribution, and uniform distribution. A thorough study on the effects of reinforcement volume fractions and porosity distribution patterns on the dynamic response of the structure has been carried out using the radial point interpolation meshfree method based on the 2D theory of elasticity. In addition, a Pareto front solution is obtained through a multiobjective optimization aimed at minimizing the weight and maximizing the natural frequency of the structure with porosity and reinforcement volume fraction as design variables. From a design perspective, the results indicate that the SYD porosity type is the best candidate for relatively thick cylinders because of its smaller mass and higher stiffness compared to the other distribution types. The current research presents a reliable computational framework to help provide an insight into the design of an optimum structure subject to dynamic loading.

Analysis of fracture mechanics and fatigue crack growth in moderately thick plates using an efficient meshfree approach

This paper presents a robust meshfree technique for computation of moment and stress intensity factors, and analysis of fatigue crack growth in cracked plates under the application of in- and out of-plane loads; a methodology for efficient and accurate computation of parameters of fracture mechanics problems is thus developed. Although having small computational labor and few complications of formulation, the proposed method has a high accuracy and convergence rate. By adding a few nodes in the vicinity of the crack tip, instead of enriching the basis functions, the singularity of the crack-tip fields is well captured with high accuracy. Also, by employing the background decomposition method (BDM), which is an efficient method for evaluation of the domain integrals, accurate solutions are obtained with small computational labor. The stress and moment intensity factors, which are two major parameters in analysis of the crack behavior, and prediction of its growth path, are calculated using the domain form of the interaction integral. Fracture mechanics problems under static condition, as well as under fatigue condition are investigated. Applying the meshfree radial point interpolation method along with the BDM has led to not only accurate results but also small computational cost. The accuracy of the results achieved for the stress intensity factors and also fatigue life of cracked bodies under cyclic loading is assessed by comparing the computed results with those found in the literature.