Nodal Strain Research Articles

Assessment of LV structural remodelling by the application of the finite element method to 3D echocardiography data

ABSTRACT This study presents novel applications for conducting left ventricular (LV) shape analysis within a finite element (FE) framework. The 3D endocardial surface data of both healthy and dilated LVs are obtained using TomTec 4D LV-Analysis software through echocardiography and then imported into the FE framework for LV geometry. By applying FE analysis to 3D echocardiography data, we propose novel methods for evaluating LV shape and remodelling, including the nodal strain approximation along myocardial fibre directions, the assessment of LV sphericity and eccentricity in multiple planes, a new method for LV apical conicity, and the analysis of regional LV rotations. The feasibility of these novel formulations and the developed FE based framework are demonstrated by evaluating and comparing 3D echocardiography data from two objects, one with a healthy LV and the other with dilated cardiomyopathy.

Enhanced Strain Field Reconstruction in Ship Stiffened Panels Using Optical Fiber Sensors and the Strain Function-Inverse Finite Element Method

Accurately reconstructing the strain field within stiffened ship panels is crucial for effective structural health monitoring. This study presents a groundbreaking approach to strain field reconstruction in such panels, utilizing optical fiber sensors in conjunction with the strain function-inverse finite element method (SF-iFEM). A novel technique for solving nodal strain vectors, based on the element strain function, has been devised to improve the accuracy of strain reconstruction using the inverse finite element method (iFEM), addressing the limitations associated with traditional nodal displacement vector solutions. Moreover, the proposed method for determining the equivalent neutral layer of stiffened ship panels not only reduces the number of elements effectively but also establishes a strain function between the inner and outer surfaces of the structure. Using this function, a layout scheme for optical fiber sensors on the inner side of ship stiffened panels is provided, overcoming the symmetrical arrangement constraints of iFEM for sensor placement on both the inner and outer sides of the structure. The results demonstrate a significant improvement in strain reconstruction accuracy under bending and bending–torsion deformations compared to conventional iFEM. Consequently, the findings of this research will contribute to enhancing the engineering applicability of iFEM in ship structure health monitoring.

Strain/displacement field reconstruction and load identification of bracket arm structure of high-speed maglev train based on superposition conversion algorithm

The bracket arm structure, subjected to long-term vertical levitation and transversal guidance forces, is a key load-bearing component of high-speed maglev trains. It is crucial to monitor strain, displacement, and load in real time to evaluate structural health. However, it is almost impossible to measure directly at the service site of trains due to the intricacy of the bracket arm structure and the constrained installation area. Hence, it is an effective and feasible approach to reconstruct the strain/displacement field using a limited amount of strain information from FBG sensors. In order to reconstruct the strain/displacement field and identify the load on complicated structures, a load–strain/displacement superposition conversion algorithm is proposed in this paper. The modal coordinate and the mode-shape matrix are swapped out for the load weight and the load–strain/displacement matrix, respectively. Thus, it gets around the difficulty of choosing the mode order in traditional modal theory. In addition, the algorithm can achieve full-field reconstruction of both strain and displacement by measuring only part of the nodal strain response, reducing the redundancy of the traditional algorithm. Finally, numerical simulations and experimental tests were carried out to verify the feasibility of the proposed method for field reconstruction and load identification.

Augmenting low‐order finite element method with partial nodal strain smoothing for flow‐deformation analysis of geomechanical problems

AbstractIn this study, the application of a numerical technique referred to as partial node‐based smoothed finite element method (PNS‐FEM) in flow‐deformation analysis of problems in geomechanics is presented. The PNS‐FEM is developed by augmenting the computation of the stiffness and permeability matrices of the domain in the linear finite element method (FEM) with partial nodal strain smoothing. The PNS‐FEM takes advantage of contradicting errors of the solutions of the linear FEM and the node‐based smooth point interpolation method (NSPIM) to yield close‐to‐exact solutions. The formulation of the PNS‐FEM and the steps required to develop a PNS‐FEM code from an FEM code are thoroughly presented. The performance of the PNS‐FEM is then examined through five numerical examples concerning linear and nonlinear porous materials undergoing various types of loading. The results show that partial nodal smoothing is a very simple, yet effective, technique to considerably improve the performance of the linear FEM in coupled problems of geomechanics.

A nodal‐based evolutionary optimization algorithm for frame structures

AbstractThis work proposes a nodal‐based evolutionary design optimization algorithm to design frame structures whose edges are the Delaunay triangulation of homogeneously distributed nodes in the design domain. The remaining nodes can freely sway in the design domain except for the loading nodes and boundary nodes. As a result, it can extend the space of admissible solutions to this optimization problem and reduce the number of design variables. Then, the sensitivity of the objective function, namely, the sum of compliance and its volume, is input into the method of moving asymptotes to update the nodal coordinates and member thickness. The most inefficient node is deleted in each iteration based on the average nodal strain energy until its number reaches a prescribed limit. 2D numerical examples for the Michell arch, L‐shaped bracket, and Messerschmidt–Bölkow–Blohm beam show that the proposed algorithm can get the optimal structure within a few iterations. Compared with initial configurations in 3D, the optimal crane arm, transmission tower, and aquatic dome have less strain energy and fewer materials, showing a great potential of the proposed method to design actual space frames.

A boundary density evolutionary topology optimization of continuum structures with smooth boundaries

AbstractBased on the variable density method, this article proposes a boundary density evolutionary topology optimization method. The method uses a material interpolation model without penalization. Combined with the density grading filtering method, an optimal topology with only 0/1 cells can be obtained. Compared with the solid isotropic microstructures with penalization method (SIMP), no penalty factor is required in the material interpolation model; compared with the evolutionary structural optimization method (ESO), intermediate‐density elements are allowed in the optimization process, but the concept of gradually removing the low‐utilization materials near the boundary in the ESO method is retained. After the optimal result is obtained, the structural boundary element is processed by the level set of nodal strain energy, and the optimization result with smooth boundaries similar to the level set method (LSM) can be obtained. The proposed method has the superiority of the variable density method, and it also combines the advantages of the evolutionary method and the level set method, so which is named as boundary density evolution (BDE) method. The four static and one dynamic optimization examples illustrate the stability and efficiency of the proposed method.

A consistent Timoshenko hysteretic beam finite element model

A parametrized Timoshenko hysteretic beam finite element model is developed, using consistent two-node elements, to efficiently simulate the nonlinear behavior of structures. New displacement interpolation functions are derived that satisfy both the exact equilibrium and kinematic conditions. Therefore, nodal strain field continuity is achieved, resulting in a consistent formulation without shear locking effects. Multiaxial interactions are considered through yield/capacity functions and distributed plasticity is accounted for by appropriate hysteretic interpolation functions. The suggested interpolation functions yield constant element matrices that do not require updating throughout the analysis, and the nonlinearities are captured in terms of hysteretic curvatures, axial and shear deformations, which are set to evolve through ordinary differential equations. A computationally efficient solution scheme is also suggested, without requiring any linearization, to straightforwardly solve the resulting system of equations for quasi-static problems. The consistency, efficiency, versatility and validity of the suggested model is explained in detail and demonstrated through several numerical examples and comparisons with experimental data from available tests.

Evaluation of High Strain Rate Characteristics of Metallic Sandwich Specimens

An attempt is made to investigate the dynamic compressive response of multilayered specimens in bilayered and trilayered configurations, using a split Hopkinson pressure bar (SHPB) and finite element analysis. Two constituent metals comprising the multilayered configurations were Al 6063-T6 and IS 1570. Multiple stack sequences of trilayered and bilayered configurations were evaluated at three different sets of strain rates, namely, 500, 800, and 1000 s−1. The experiments revealed that even with the same constituent volume fraction, a change in the stacking sequence alters the overall dynamic constitutive response. This change becomes more evident, especially in the plastic zone. The finite element analysis was performed using abaqus/explicit. A three-dimensional (3D) model of the SHPB apparatus used in the experiments was generated and meshed using the hexahedral brick elements. Dissimilar material interfaces were assigned different dynamic coefficients of friction. The fundamental elastic one-dimensional (1D) wave theory was then utilized to evaluate the stress–strain response from the nodal strain histories of the bars. Predictions from the finite element simulations along with the experimental results are also presented in this study. For most cases, finite element predictions match well with the experiments.

Adaptive simultaneous motion and vibration control for a multi flexible-link mechanism with uncertain general harmonic disturbance

In this paper, a new motion and vibration synthesized control system—a linear quadratic regulator/strain rate feedback controller (LQR/SRF) with adaptive disturbance attenuation is presented for a multi flexible-link mechanism subjected to uncertain harmonic disturbances with arbitrary frequencies and unknown magnitudes. In the proposed controller, nodal strain rates are introduced into the model of the multi flexible-link mechanism, based upon which a synthesized LQR controller where both rigid-body motion and elastic deformation are considered is designed. The uncertain harmonic disturbances would be canceled in the feedback loop by its approximated value which is computed online via an adaptive update law. Asymptotic stability of the closed-loop system is proved by the Lyapunov analysis. The effectiveness of the proposed controller is shown via simulation.

A Hybrid Interpolation Method for Geometric Nonlinear Spatial Beam Elements with Explicit Nodal Force

Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by using the hybrid interpolation. Furthermore, the proposed beam element can be degenerated into linear beam element under the condition of small deformation. Objectivity of strain measures and patch tests are also discussed. Finally, four numerical examples are discussed to prove the validity and effectivity of the proposed beam element.

Nodal versus Total Axonal Strain and the Role of Cholesterol in Traumatic Brain Injury.

Traumatic brain injury (TBI) is a health threat that affects every year millions of people involved in motor vehicle and sporting accidents, and thousands of soldiers in battlefields. Diffuse axonal injury (DAI) is one of the most frequent types of TBI leading to death. In DAI, the initial traumatic event is followed by a cascade of biochemical changes that take time to develop in full, so that symptoms may not become apparent until days or weeks after the original injury. Hence, DAI is a dynamic process, and the opportunity exists to prevent its progression provided the initial trauma can be predicted at the molecular level. Here, we present preliminary evidence from micro-finite element (FE) simulations that the mechanical response of central nervous system myelinated fibers is dependent on the axonal diameter, the ratio between axon diameter and fiber diameter (g-ratio), the microtubules density, and the cholesterol concentration in the axolemma and myelin. A key outcome of the simulations is that there is a significant difference between the overall level of strain in a given axonal segment and the level of local strain in the Ranvier nodes contained in that segment, with the nodal strain being much larger than the total strain. We suggest that the acquisition of this geometric and biochemical information by means of already available high resolution magnetic resonance imaging techniques, and its incorporation in current FE models of the brain will enhance the models capacity to predict the site and magnitude of primary axonal damage upon TBI.

The topology optimization design for cracked structures

In this paper, the element free Galerkin method (EFG) is proposed for topology optimization of cracked structures using the bi-directional evolutionary structural optimization method (BESO). The mathematical formulation of the topology optimization is developed considering the nodal strain energy as the design variable and the minimization of compliance as the objective function. The element free Galerkin method is enriched by the crack-tip enrichment functions to increase the approximation accuracy near the crack-tip. The Lagrange multiplier method is employed to enforce the essential boundary conditions. Several numerical examples are presented to show the effectiveness of the proposed method. Many issues related to topology optimization of cracked structures such as the effects of crack size and location on the optimal topology are addressed in the examples. The common numerical instabilities do not exist in the results.

Topology optimization using bi-directional evolutionary structural optimization based on the element-free Galerkin method

In this article, the bi-directional evolutionary structural optimization (BESO) method based on the element-free Galerkin (EFG) method is presented for topology optimization of continuum structures. The mathematical formulation of the topology optimization is developed considering the nodal strain energy as the design variable and the minimization of compliance as the objective function. The EFG method is used to derive the shape functions using the moving least squares approximation. The essential boundary conditions are enforced by the method of Lagrange multipliers. Several topology optimization problems are presented to show the effectiveness of the proposed method. Many issues related to topology optimization of continuum structures, such as chequerboard patterns and mesh dependency, are studied in the examples.

Simulation of fracture/breakup of concrete magazine using cohesive element

To determine the potential hazard zone around an ammunition storage magazine is the research interest of many researchers working on explosive safety. Carrying out an explosion test of an ammunition storage magazine is expensive. As such, numerical modeling offers an economical solution to supplement the field tests, and it has been widely used to simulate the magazine breakup. In the literature and own previous studies, numerical simulations often resorted to the Lagrangian finite‐element method and used the nodal‐split algorithm to model the concrete fracture/breakup upon internal detonation. Pitfalls in that approach have not been fully recognized [–]. In it, all elements initially connected to the same node would be spilt in all directions once the nodal strain reached the threshold. This strain‐based splitting criterion lacks of sound physical meaning. To overcome those pitfalls, the present study adopts a kind of interface element, namely a cohesive element, to simulate the fracture/breakup. Strain rate dependent experiments were carried out to obtain the fracture criteria, which were then applied to define the threshold for element‐face split. Results show that it yields good agreement with experiment tests, including Split Hopkinson Pressure Bar (SHPB) on concrete specimen and breakup of concrete magazine upon detonation.

Macro-composites with star-shaped inclusions for vibration damping in wind turbine blades

The work describes the numerical and experimental assessment of using biphase composite structures with non-classical shape inclusions. Star-shaped biphase cells have been designed, modeled and tested to evaluate the complex engineering constants corresponding to various deformation modes. A Finite Element homogenisation method using the complex modulus approach has been used to evaluate the variation of the storage moduli, loss factors and amounts of strain energy dissipated in the matrix versus the unit cell geometry parameters. Experimental results have been obtained on aluminium/cast epoxy sample using a shear dynamic test rig and a dynamic mechanical analyser. The results have been benchmarked against unit biphase composite configurations with cylindrical inclusions having the same contact surface between inclusion and matrix than the star-shaped reinforcements. The composite cells are intended for a possible use as structural damping units to be located in maximum nodal strain positions corresponding to specific wind turbine blade modes.

Meshfree consolidation analysis of saturated porous media with stabilized conforming nodal integration formulation

A strain smoothing meshfree formulation with stabilized conforming nodal integration is presented for modeling the consolidation process in saturated porous media. In the present method, nodal strain smoothing is consistently introduced into the meshfree approximation of strain and pore pressure gradient variables associated with the saturated porous media. Meanwhile, in order to achieve a consistent numerical implementation, a smoothing approximation of the meshfree shape function within a nodal representative domain is also proposed in the stiffness construction. The resulting discrete system of equations is all expressed in smoothed nodal measures that are very efficient for numerical evaluation. Subsequently the space-time fully discrete equations are further established by the generalized trapezoidal rule for time integration. The effectiveness of the proposed meshfree consolidation analysis method is systematically illustrated by several benchmark problems.

Application of Strain Mode Difference in the Damaged Beam Damage Detection

For the beam with certain degree, it was difficult to reflect by displacement modal and natural frequency. The present paper first derived nodal strain modal through its corresponding displacement modal, and then evaluates the strain modal, both prior and post damage, the difference between the strain mode was used as a criterion to assess the damage experienced, based on a simple beam element damage localization method. The formulated method had been demonstrated through ANSYS numerical modeling to be capable of effectively identifying the damage.

An Adaptive Element-Free Galerkin Method Based on the Strain Energy Density

In practical study, an adaptive procedure based on the gradient of the strain energy density is developed for element-free Galerkin method using moving least-squares (MLS) approximation and global Galerkin formulation require a background mesh for domain integration. It comprises nodal strain energy density and a local domain refinement technique. The numerical experiments in this paper show that this adaptive element-free Galerkin method is simple, effective and efficient.

A displacement-based finite element formulation for the analysis of laminated composite plates

This paper presents the nodally integrated plate element (NIPE) formulation for the analysis of laminated composite plates based on the first-order shear deformation theory. The nodally integrated approach aims at providing smoothed derivative quantities by constructing nodal strain–displacement operators. Within this framework a new family of elements for plates with general monoclinic layers is developed: the strain–displacement operators are derived via nodal integration for linear triangles and quadrilateral elements. The degrees of freedom are only the primitive variables: displacements and rotations at the nodes. The NIPEs are locking-free elements, exhibit little sensitivity to geometric distortions and can be readily implemented into existing finite element codes. The efficiency of the proposed variational formulation is proved whereas effectiveness and convergence of the proposed finite elements are confirmed through several numerical applications. Finally, numerical results are compared with the corresponding analytical solutions as well as to other finite-element solutions.

A stabilized formulation for discrete gradient method

AbstractThis paper presents a stabilization scheme for the discrete gradient method proposed by the authors (Int. J. Numer. Methods Eng. 2009; 78:505–527). The discrete method is an extension of the nodal average strain triangle element to arbitrary polygon meshes. The method outperforms the low‐order finite elements in many aspects; however, it is susceptible to spurious zero‐energy or low‐energy modes arising from cancelation of strains during strain averaging. In this paper, stabilization is achieved by a penalty scheme that penalizes the difference between the nodal strain and the subcell strains. Several examples, including an analytical dispersion analysis, are presented to demonstrate the stabilization effect. Copyright © 2009 John Wiley & Sons, Ltd.