Radial Point Interpolation Method Research Articles

RPIM-RITSS Method for Large Deformation Analysis Using ABAQUS

In the standard Lagrangian finite-element framework, the “remeshing and interpolation technique with the small strain” (RITSS) method has been applied increasingly in geotechnical engineering. However, the mapping algorithm of the RITSS method suffers from either the onerous division of unique element, such as the modified unique element divisional method, or frequent mapping of the stress and other information between integration points and nodes, resulting in the loss of precision, such as superconvergent patch recovery (SPR) and recovery by equilibration of patches. In this study, within the original RITSS, the radial point interpolation method (RPIM) mapping algorithm is implemented to improve accuracy and convenience. The RPIM-RITSS method is integrated into the ABAQUS (6.14) commercial software package. With a master Python script, the whole analysis process is performed automatically and continuously without any intervention from the user. The efficiency and robustness of the RPIM-RITSS method are verified through three numerical examples: penetration of the strip footing, the pullout and the rotation of the anchor plate, and deep penetration of the T-Bar. Consequently, the RPIM-RITSS method is an alternative, powerful, and easily extensible way to tackle large deformation problems in geotechnical engineering.

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.

Variable RPIM and HOCM coupling for non-linear buckling and post-buckling analysis of transverse FG sandwich beams

This paper presents an analytical-based approach to analyze non-linear buckling and post-buckling of transverse functionally graded sandwich beams (TFGSB). The proposed approach combines a high order continuation method (HOCM) and a variable radial point interpolation method (RPIM). First of all, the strong form of the beam buckling governing equations are established in the framework of first order shear deformation theory (FSDT) by taking into account the non-linear tangential term. Then, the spatial approximation of the unknown variables and their partial derivatives using the RPIM with variable shape parameters is the first step of this approach. The RPIM shape parameter is considered to change according to Franke formula, modified Franke formula or reciprocal Franke formula. The non-linear resulting system of discrete equations is linearized by using the Taylor series expansion, whilst the continuation method is employed to obtain the whole solution. To demonstrate the effectiveness of the proposed approach, numerical examples on non-linear buckling and post-buckling analysis of TFGSB are presented. These numerical tests are carried out to define the optimal RPIM with variable shape parameters and to investigate the sensitivity of the accuracy regarding boundary conditions, effects of power-law index, Young’s modulus, skin-core-skin thickness and the span-depth ratios. The results obtained through the proposed approach are compared with those computed by finite element method (FEM) and the available data in the literature.

An inhomogeneous stabilized node-based smoothed radial point interpolation method for the multi-physics coupling responses of functionally graded magneto-electro-elastic structures

In this paper, an inhomogeneous stabilized node-based smoothed radial point interpolation method (ISNS-RPIM) is developed for analyzing functionally graded magneto-electro-elastic (FGMEE) structures in hygrothermal environment. The change of material gradient follows the exponential function distribution. Combining with the gradient smoothing technique (GST) and the coupling constitutive relationship, and considering the hygrothermo-magneto-electro-elastic (HMEE) coupling effects of FGMEE material, the equations for ISNS-RPIM are deduced. The generalized displacement of the FGMEE structures is obtained, and the error in total energy norm, CPU time and efficiency of ISNS-RPIM, NS-RPIM and FEM are researched. Numerical examples are provided to explore the influence of the following parameters in FGMEE structures including exponential factor, hygrothermal loading and empirical constants, and demonstrate the correctness, high effectivity and insensitivity to mesh distortion of ISNS-RPIM. The present method has shown great potential in solving practical complex problems.

Free vibration parametric study of a single lap joint using the Radial Point Interpolation Method

Free vibration parametric study of a single lap joint using the Radial Point Interpolation Method

Total knee arthroplasty coronal alignment and tibial base stress-a new numerical evaluation.

Total knee arthroplasty (TKA) is one of the most frequently performed orthopedic procedures. The correct positioning and alignment of the components significantly affects prosthesis survival. Considering the current controversy regarding the target of postoperative alignment of TKA, this study evaluated the tension at tibial component interface using two numerical methods. The stress of the prosthesis/bone interface of the proximal tibial component was evaluated using two numerical methods: the finite element method (FEM) and the new meshless method: natural neighbor radial point interpolation method (NNRPIM). The construction of the model was based on Zimmers NexGen LPS-Flex Mobile® prosthesis and simulated the forces by using a free-body diagram. Tibiofemoral mechanical axis (TFMA) for which a higher number of nodes are under optimal mechanical tension is between 1° valgus 2° varus. For values outside the interval, there are regions under the tibial plate at risk of bone absorption. At the extremities of the tibial plate of the prosthesis, both medial and lateral, independent of the alignment, are under a low stress. In all nodes evaluated for all TFMA, the values of the effective stresses were higher in the NNRPIM when compared with the FEM. Through this study, we can corroborate that the optimal postoperative alignment is within the values that are currently considered of 0 ± 3° varus. It was verified that the meshless methods obtain smoother and more conservative results, which may make them safer when transposed to the clinical practice.

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

Highly efficient mesh-free approach to simulate the non-linear bending analysis of FG porous beams and sandwich beams with FG face sheets

The main objective of the present work is to propose a coupling of the Radial Point Interpolation Method (RPIM) with variable shape parameter to High Order Continuation Method (HOCM) for analyzing the geometrically non-linear behavior of porous Functionally Graded (FG) isotropic and sandwich Timoshenko beams by taking into account the non-linear shear deformation. The FG and FG Sandwich Beams (FGSB) effective material properties are assumed to vary continuously in the thickness direction according to a power-law index. The porosity is modeled as the stiffness reduction criteria and included in the mixture rule. The strong form of the non-linear equations governing porous FG and FGSB beams are obtained using the principle of virtual displacements in the framework of First-Order Shear Deformation Theory (FOSDT). The HOCM is used to compute the solution of the non-linear problem by a transformation to recursive succession of linear problems using Taylor series expansion. The continuation technique is used to obtain the complete solution path in a step by step manner. The effectiveness and accuracy of the proposed coupling is brought out through numerical examples which concern porous FG isotropic and FG sandwich beams. The optimal parameters have been defined according to the stability analysis of the proposed solver, and then used to investigate the effect of boundary conditions, showing the effect of the power-law index, effect of geometric imperfections, and face sheet-core-face sheet thickness ratios on deflections. The validation is done by comparing the obtained results to those available in the literature and/or those computed using Finite Element Method (FEM).

On Interpolative Meshless Analysis of Orthotropic Elasticity

As one possible alternative to the finite element method, the interpolation characteristic is a key property that meshless shape functions aspire to. Meanwhile, the interpolation meshless method can directly impose essential boundary conditions, which is undoubtedly an advantage over other meshless methods. In this paper, the establishment, implementation, and horizontal comparison of interpolative meshless analyses of orthotropic elasticity were studied. In addition, the radial point interpolation method, the improved interpolative element-free Galerkin method and the interpolative element-free Galerkin method based on the non-singular weight function were applied to solve orthotropic beams and ring problems. Meanwhile, the direct method is used to apply the displacement boundary conditions for orthotropic elastic problems. Finally, a detailed convergence study of the numerical parameters and horizontal comparison of numerical accuracy and efficiency were carried out. The results indicate that the three kinds of interpolative meshless methods showed good numerical accuracy in modelling orthotropic elastic problems, and the accuracy of the radial point interpolation method is the highest.

Dispersion error control for underwater acoustic scattering problems using a coupled cell-based smoothed radial point interpolation method

A coupled cell-based smoothed radial point interpolation method is presented by combining the cell-based smoothed radial point interpolation method (CSRPIM) and the modified Dirichlet to Neumann boundary condition (MDtN-BC) to effectively control the dispersion error in predicting acoustic scattering. In the coupled CSRPIM, the MDtN-BC is used to satisfy the Sommerfeld radiation condition approaching infinity, and a cell-based smoothing operation together with the radial point interpolation method (RPIM) is adopted to soften the acoustic stiffness of the numerical model. The condensed RPIM shape functions are created by using real and virtual nodes, and virtual node selection schemes are studied to appropriately soften the stiffness. A major advantage of the coupled CSRPIM is that it can achieve very close-to-exact stiffness of the original model without introducing extra degrees of freedom. The properties of the proposed method are numerically studied. Simulations indicate that the six-virtual-node selection scheme performs the best. The results reveal that the developed method can significantly reduce the dispersion error and has excellent computational performance. In addition, the developed method shows good potential for practical acoustic-scattering prediction in engineering applications.

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.

Analysis of cracked Reissner-Mindlin plate using an extended meshfree method

An extended meshfree method for analyzing cracked plates based on Reissner-Mindlin theory is presented in this paper. Among a variety of meshfree formulations, the radial point interpolation method (RPIM) is chosen in this study due to the satisfaction of the Kronecker delta property. The essential boundary conditions, therefore, are easily imposed in the RPIM. The shape function derived from RPIM is employed to interpolate the field variables. An extended RPIM formulation is used to model the crack segment without explicitly defining it in the discretized domain. The discontinuity due to the crack is defined by extrinsic enriched functions, particularly, the jump in the displacement field on two sides of the crack is modelled by the Heaviside function, and the stress singularity near the crack tip is described by the asymptotic enriched function. In this study, the stress resultant intensity factors (SRIFs) are evaluated through the interaction integral approach. The obtained SRIFs are shown in the paper through many numerical examples for comparison purposes. The trending variation of SRIFs is also observed from the numerical results. It can be remarked that the SRIFs depend on many factors: the number of cracks, crack orientation, load type and boundary conditions. The numerical examples show the accuracy of the present approach. The obtained results are compared with analytical solutions and other numerical methods.

Application of Random Radial Point Interpolation Method to Foundations Bearing Capacity Considering Progressive Failure

In conventional analyzes of foundations failure, strengh parameters are assumed constant. However, during the failure, soil resistance exhibits maximum and residual amounts, and its strength decreases prematurely by increasing the plastic strain. In addition to change soil strengh parameters in the progressive mechanism, the non-uniform nature of the soil also causes spatial variations of these parameters. Therefore, geotechnical systems should be considered in terms of the uncertainty of soil parameters values, uncertainly using the concepts of statistics and probabilities. The purpose of this study is to investigate foundations in meshless method. In this article, radial point interpolation method (RPIM), a meshless method is proposed for simulation of soil foundation. Difficulties of methods related to mesh are solved by using this method. A code has been developed based on this method and some examples are solved for analyzing the code. In this research, a RPIM in combination with a random field was used to model the spatial variations of soil strengh properties and foundation bearing capacity analysis. For probabilistic analysis, random field is also used to determine the cohesion and the friction angle as well as the dilation angle based on their mean values and standard deviation. In order to investigate the application of the point interpolation method with randomized radial functions, a foundation with definite geometry has been analyzed deterministic and probabilistic and its safety factor has been investigated. Based on the analysis of the progressive failure modeling, it is concluded that the actual failure of the soil and the occurrence of continuous displacements occur simultaneously with the formation of a progressive mechanism of soil failure and the arrival of the slipping path to the ground. In the following, probabilistic distribution functions of the safety factor were determined by probabilistic analysis and the production of random fields, and then the statistical parameters are calculated.

Free Vibration Analysis of Curved Shell Structures with Various Boundary Conditions by Using A Meshfree Method

In this paper, the free vibration of curved shell structures with various boundary conditions is examined by using a meshfree method. The meshfree method in this study is based on the radial point interpolation method (RPIM). The RPIM shape function is chosen because it satisfies the Kronecker delta property allowing for the direct imposition of essential boundary conditions. The field variables and the geometry of the curved shell are interpolated through the RPIM shape function. The curved shell formulation is constructed based on the first-order shear deformation theory (FSDT), which considers the transverse shear strain. In a meshfree approach to investigate curved shell structures, a convected coordinate system is employed. This convected coordinate system is tied to the curved surface and used to map an arbitrary curved shell in 3D space into 2D space. To obtain the numerical solution, the calculation is performed first in this convected coordinate system and then mapped back to the global coordinate system. The accuracy and ability of the meshfree method have been shown through many numerical examples. The natural frequencies of curved shells with different geometry and boundary conditions are in good agreement with other available reference solutions.

Crack Analysis by Using An Extended Meshfree Method and Cartesian Transformation Method without Creating Subdomains

This paper investigates the fracture behavior of plates with through-thickness crack by using the extended concept of the Radial Point Interpolation Method (RPIM). The attractiveness of the RPIM shape functions is the satisfaction of the Kronecker delta property providing direct imposition of essential boundary conditions. In the extended concept, the jump in deflection and rotation fields caused by crack, also the stress singularity near the crack tip are described by adding enriched functions to the interpolation equation. Particularly, Heaviside function and asymptotic enriched function. For numerical integration, the Cartesian Transformation Method (CTM) is employed. No integration background cell is required in CTM, this technique transforms a domain integral into a boundary integral and a 1D integral. For analysis of discontinuous problems, in this study, the distribution of integration points is manipulated to avoid the discontinuity caused by crack segmentation. Therefore, no subdomains are required, unlike other reference CTM studies. To achieve that, a virtual boundary is introduced that represents the discontinuity such as holes or cracks. This also matches the concept of the extended approach that no explicit discontinuity exists in the geometry, instead, the discontinuity is modelled by mathematics equation. The Stress Intensity Factors (SIFs) of the cracked plate are evaluated through the interaction integral technique. The efficiency of the proposed method is illustrated through various numerical examples. The accuracy of the obtained results are compared with other available numerical solutions and analytical solutions.

The Ogden model and the natural neighbour radial point interpolation method for hyperelastic analyses

The Ogden model and the natural neighbour radial point interpolation method for hyperelastic analyses

Adaptive Anisotropy Optimization Method for the Radial Point Interpolation Method in Lossy Media

Adaptive Anisotropy Optimization Method for the Radial Point Interpolation Method in Lossy Media

Bending analysis of antisymmetric angle-ply laminates using HSDTs and the radial point interpolation method – Part I: Literature review and formulation

Bending analysis of antisymmetric angle-ply laminates using HSDTs and the radial point interpolation method – Part I: Literature review and formulation

Can global longitudinal strain (GLS) with magnetic resonance prognosticate early cancer therapy-related cardiac dysfunction (CTRCD) in breast cancer patients, a prospective study?

PurposeTo determine if Artificial Intelligence-based computation of global longitudinal strain (GLS) from left ventricular (LV) MRI is an early prognostic factor of cancer therapy-related cardiac dysfunction (CTRCD) in breast cancer patients. The main hypothesis based on the patients receiving antineoplastic chemotherapy treatment was CTRCD risk analysis with GLS that was independent of LV ejection fraction (LVEF). MethodsDisplacement Encoding with Stimulated Echoes (DENSE) MRI was acquired on 32 breast cancer patients at baseline and 3- and 6-month follow-ups after chemotherapy. Two DeepLabV3+ Fully Convolutional Networks (FCNs) were deployed to automate image segmentation for LV chamber quantification and phase-unwrapping for 3D strains, computed with the Radial Point Interpolation Method. CTRCD risk (cardiotoxicity and adverse cardiac events) was analyzed with Cox Proportional Hazards (PH) models with clinical and contractile prognostic factors. ResultsGLS worsened from baseline to the 3- and 6-month follow-ups (−19.1 ± 2.1%, −16.0 ± 3.1%, −16.1 ± 3.0%; P < 0.001). Univariable Cox regression showed the 3-month GLS significantly associated as an agonist (hazard ratio [HR]-per-SD: 2.1; 95% CI: 1.4–3.1; P < 0.001) and LVEF as a protector (HR-per-SD: 0.8; 95% CI: 0.7–0.9; P = 0.001) for CTRCD occurrence. Bivariable regression showed the 3-month GLS (HR-per-SD: 2.0; 95% CI: 1.2–3.4; P = 0.01) as a CTRCD prognostic factor independent of other covariates, including LVEF (HR-per-SD: 1.0; 95% CI: 0.9–1.2; P = 0.9). ConclusionsThe end-point analyses proved the hypothesis that GLS is an early, independent prognosticator of incident CTRCD risk. This novel GLS-guided approach to CTRCD risk analysis could improve antineoplastic treatment with further validation in a larger clinical trial.

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&lt;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&lt;0.001) and LVEF as protector (HR-per-SD: 0.8; 95% CI: 0.7-0.9, P&lt;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.