Element Distortion Research Articles

A High-Precision Inverse Finite Element Method for Shape Sensing and Structural Health Monitoring

In the contemporary era, the further exploitation of deep-sea resources has led to a significant expansion of the role of ships in numerous domains, such as in oil and gas extraction. However, the harsh marine environments to which ships are frequently subjected can result in structural failures. In order to ensure the safety of the crew and the ship, and to reduce the costs associated with such failures, it is imperative to utilise a structural health monitoring (SHM) system to monitor the ship in real time. Displacement reconstruction is one of the main objectives of SHM, and the inverse finite element method (iFEM) is a powerful SHM method for the full-field displacement reconstruction of plate and shell structures. However, existing inverse shell elements applied to curved shell structures with irregular geometry or large curvature may result in element distortion. This paper proposes a high-precision iFEM for curved shell structures that does not alter the displacement mode of the element or increase the mesh and node quantities. In reality, it just modifies the methods of calculation. This method is based on the establishment of a local coordinate system on the Gaussian integration point and the subsequent alteration of the stiffness integration. The results of numerical examples demonstrate that the high-precision iFEM is capable of effectively reducing the displacement difference resulting from inverse finite element method reconstruction. Furthermore, it performs well in practical engineering applications.

Comprehensive investigation on modelling of low-velocity impact damage response of composite laminates − Experimental correlation and assessment

Low velocity impact (LVI) experiments are performed to provide correlations with the simulation results based on numerical modeling of the intralaminar matrix damage and interlaminar delamination damage of composite laminates. The good agreement between the numerical simulation and experimental results provided validation of the numerical modeling approach. The validated numerical modeling is then used in the parametrical assessment of the influence of material properties and model- related parameters on the global LVI deformation responses and the evolution characteristics of the intralaminar and interlaminar damage. It is observed that the element deletion method is not suitable to resolve the element distortion problem induced by the progressive damage. The numerical convergence problem caused by element distortion can be resolved with appropriate selection of threshold value of the critical damage parameter without element deletion. The parametrical numerical investigations showed that the variations of material properties and parameters related to interlaminar damage exhibited significant influence on the LVI global deformation responses and progressive damage evolutions. Meanwhile, insignificant influence of the material properties related to the intralaminar damage was observed for the normal variations within material scatters.

A diffusive‐discrete crack transition scheme for ductile fracture at finite strain

SummaryThis study presents a diffusive‐discrete crack transition scheme for stably conducting ductile fracture simulations within a finite strain framework. In the developed scheme, the crack initiation and propagation processes are determined according to an energy minimization problem based on crack phase‐field theory, and the predicted diffusive path is transformed to a discrete representation using the finite cover method during the staggered iterative scheme. In particular, for stably conducting ductile fracture simulations, three computational techniques, the staggered iterative configuration update technique, the subincremental damage update technique, and the crack opening stabilization technique, are introduced. The first and second techniques can be used regardless of whether discrete cracks are considered, and the third technique is specialized for diffusive‐discrete crack transition schemes. Accordingly, ductile fracture simulations with the developed scheme rarely encounter troublesome problems such as oscillations in the displacement field and severe distortion of finite elements that can lead to divergence of calculations. After the crack phase‐field model for ductile fractures is formulated and discretized, the numerical algorithms for realizing the diffusive‐discrete crack transition while maintaining computational stability are explained. Several representative numerical examples are presented to demonstrate the performance and capabilities of the developed approach.

An interface constitutive model of plastic tensile–compressive damage under impact loading based on continuous–discontinuous framework

Bullet penetration test is a classic impact loading test, which involves complex dynamic elastic–plastic response. Conventionally, this process was often described using a single high-strain-rate constitutive model, which could only capture a specific type of failure during the impact damage process. Furthermore, these constitutive models were mostly defined on element and posed the risk of computational divergence(element distortion). In this work, a novel constitutive model for combined tensile–compressive damage in interface element was developed within a Continuous–Discontinuous Element Method(CDEM) framework. This model successfully captures the processes of pit formation and target collapse during projectile penetration. The tension and compression damage parts of the developed interface constitutive model were validated through Brazilian splitting test and interface direct shear test. Subsequently, bullet penetration test is simulated and the post-penetration velocity is compared with published results from other studies, with computational errors found to be within 2.56%, thus validating the accuracy of the developed interface constitutive model.

A Hu-Washizu variational approach to self-stabilized quadrilateral Virtual Elements: 2D linear elastodynamics

A recent mixed formulation of the Virtual Element Method in 2D elastostatics, based on the Hu-Washizu variational principle, is here extended to 2D elastodynamics. The independent modeling of the strain field, allowed by the mixed formulation, is exploited to derive first order quadrilateral Virtual Elements (VEs) not requiring a stabilization (namely, self-stabilized VEs), in contrast to the standard VEs, where an artificial stabilization is always required for first order quads. Lumped mass matrices are derived using a novel approach, based on an integration scheme that makes use of nodal values only, preserving the correct mass in the case of rigid-body modes. In the case of implicit time integration, it is shown how the combination of a self-stabilized stiffness matrix with a self-stabilized lumped mass matrix can produce excellent performances both in the compressible and quasi-incompressible regimes with almost negligible sensitivity to element distortion. Finally, in the case of explicit dynamics, the performances of the different types of derived VEs are analyzed in terms of their critical time-step size.

Modeling of 2D thermo-elastic brittle fracture using smoothed floating node method

This paper presents an extension of the recently developed smoothed floating node method (SFNM) with cohesive zone approach to model crack growth in elastic materials under thermo-elastic loading conditions. The SFNM utilizes floating nodes to accurately model the crack by activating dormant nodes at intersection points of crack path and the corresponding element edges. Through the activation of floating nodes, the cracked element transforms into sub-elements, facilitating separate integration of each sub-element. A smoothing cell-based integration technique is employed to convert the area integral to line integral which mitigates the element distortion issues. The temperature distribution is initially determined across the entire domain, and then imposed as thermal loads in the 2D domain. The thermal stress intensity factor is calculated for both homogeneous and bi-material specimens using the interaction energy integral approach, and the crack propagation is predicted using circumferential stress criterion. The accuracy of the proposed framework is demonstrated with several benchmark problems of fracture mechanics. The develop framework yields comparable results with the available literature with less modeling complexity.

An improved Lagrange-based numerical model for machining Ti-6Al-4V alloy concerning tool cutting edge microgeometry

Current Lagrange-based machining models usually involve a sacrificial layer (LAG-SL) to facilitate the chip formation. Otherwise, severe element distortion error arises especially when tool cutting edge microgeometry is considered. In view of this limitation, an improved Lagrange-based machining model is proposed that acquires no sacrificial layer (LAG-nSL) and can simulate completely the cutting, unloading and cooling process. Through comparisons with plenty of experimental measurements, the presented model is found not only applicable for machining using tool with various edge radii, but also yields better outcomes of chip morphologies, forces and residual stress distribution.

Stress projection procedure for the form-finding analysis of membrane structures

This study examines the form-finding analysis of membrane structures and presents a new general method for determining prestress called stress projection. This method addresses several deficiencies while performing the form-finding analysis, especially in the case of conical membrane structures. A key feature of the proposed stress projection procedure is the adoption of a generally oriented projection plane, where finite elements are projected onto, and the determination of their stress states, which allows for a smooth adaptation of stresses over the membrane structures. Deformation gradients are then evaluated with respect to this projection plane, as opposed to the inertial reference frame used for the computation of stress tensors in subsequent form-finding processes.The proposed stress projection procedure efficiently modifies the stresses over the structures and significantly addresses intrinsic element distortion problems within the form-finding analysis. Thus, the proposed method allows for the maintenance of regularized finite element shapes and the smooth changing of stress states throughout form-finding iteration processes, especially for conical membrane shapes. Numerical experiments demonstrate the efficiency of the implemented stress projection scheme compared with two well-known stress adaptation schemes.

Singularity Structure Optimization for Hexahedral Mesh Via Dual Operations

Abstract This paper presents an improved method for optimizing the singularity structure of hexahedral meshes using various dual operations. Our approach aims at reducing element distortion by decomposing complex singular nodes into singular curves using high-quality sheet insertion at proper locations. Then, singular curves that meet the topological parallel requirements are paired to perform the semantic column operation, which eliminates the singular curves. Finally, the topological structure is further optimized by collapsing sheets, resulting in a valid hex mesh with a simpler structure. Compared to existing hexahedral mesh simplification methods, our approach can generate higher quality meshes. Experimental results demonstrate the effectiveness of the proposed method.

Influence of optical surface distortion in a cylindrical Offner stretcher on the far-field signal-to-noise ratio.

In a stretcher, the surface distortion of the optical elements can introduce spectral phase modulations into the laser, which can affect the laser's signal-to-noise ratio. In this paper, by combining ray tracing methods and angular spectrum diffraction methods, the impact of the mid-frequency surface distortion of the optical elements in an cylindrical Offner stretcher on the far-field signal-to-noise ratio of the laser is simulated. The results show that reducing the spatial chirp on the convex cylindrical mirror can effectively improve the far-field signal-to-noise ratio of the laser, and two methods to improve the far-field signal-to-noise ratio are presented.

Finite strain topology optimization with nonlinear stability constraints

This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to low-density elements is proposed. The strategy depends on constructing a pseudo-mass matrix that assigns small pseudo masses for DOFs surrounded by only low-density elements and degenerates to an identity matrix for the solid region. A novel optimization procedure is developed that can handle both simple and multiple eigenvalues wherein consistent sensitivities of simple eigenvalues and directional derivatives of multiple eigenvalues are derived and utilized in a gradient-based optimization algorithm — the method of moving asymptotes. An adaptive linear energy interpolation method is also incorporated in nonlinear analyses to handle the low-density elements distortion under large deformations. The numerical results demonstrate that, for systems with either low or high symmetries, the nonlinear stability constraints can ensure structural stability at the target load under large deformations. Post-analysis on the B-spline fitted designs shows that the safety margin, i.e., the gap between the target load and the 1st critical load, of the optimized structures can be well controlled by selecting different stability constraint values. Interesting structural behaviors such as mode switching, and multiple bifurcations are also demonstrated.

Numerical Study on Asteroid Deflection by Penetrating Explosion Based on Single-Material ALE Method and FE-SPH Adaptive Method

An asteroid impact can potentially destroy life on this planet. Therefore, asteroids should be prevented from impacting the Earth to impede severe disasters. Nuclear explosions are currently the only option to prevent an incoming asteroid impact when the asteroid is large or the warning time is short. However, asteroids exist in an absolute vacuum, where the explosion energy propagation mechanism differs from that in an air environment. It is difficult to describe this process using standard numerical simulation methods. In this study, we used the single-material arbitrary Lagrangian–Eulerian (ALE) method and the finite element-smoothed particle hydrodynamics (FE-SPH) adaptive method to simulate the process of deflecting hazardous asteroids using penetrating explosions. The single-material ALE method can demonstrate the expansion process of explosion products and energy coupling in absolute vacuum. The FE-SPH adaptive method can transform failed elements into SPH particles during the simulation, avoiding system mass loss, energy loss, and element distortion. We analyzed the shock initiation and explosion damage process and obtained an effective simulation of the damage evolution, stress propagation, and fragment distribution of the asteroid. In addition, we decoupled the penetrating explosion into two processes: kinetic impact and static explosion at the impact crater. The corresponding asteroid damage modes, velocity changes, and fragmentation degrees were simulated and compared. Finally, the high efficiency of the nuclear explosion was confirmed by comparing the contribution rates of the kinetic impact and nuclear explosion in the penetrating explosion scheme.

Mesoscale modelling of progressive damage and failure in single-lap and double-lap thin-ply laminated composite bolted joints

Composite bolted joints are being used extensively in primary load-bearing structures of modern aircrafts. However, simulating progressive damage and failure of the bolted composite structures under high bearing loading is still challenging. In this paper, numerical simulation and experimental verification on the bearing failure of single-lap and double-lap thin-ply laminated composite bolted joints were carried out for the entire loading process. 3D explicit finite element models have been developed using Abaqus/Explicit together with a 3D physically-based intralaminar damage model implemented in a VUMAT subroutine. An interface cohesive-zone model based on the Benzeggagh-Kenane (B-K) law was used to simulate delamination initiation and evolution. For the intralaminar damage, the initiation was determined based on Pinho’s failure criteria while the evolution was regularized with the crack-band approach to alleviate mesh-size dependence. Element deletion and in-situ effect as practical numerical strategy are discussed and analyzed in detail. Element deletion is used to prevent excessive element distortion and capture corresponding post-peak bearing failure behavior. In-situ effect has been proved to have a key influence on the damage initiation and progression of thin-ply composite matrix. The final simulation results are shown to agree well with experimental data and reproduce the mechanical response curves. More importantly, the model can accurately capture the local crushing of bolt hole in the later loading stage. This study shows that the numerical model can be helpful for the design and optimization of composite bolted structures.

HiDeNN-FEM: A seamless machine learning approach to nonlinear finite element analysis.

The hierarchical deep-learning neural network (HiDeNN) (Zhang et al, Computational Mechanics, 67:207-230) provides a systematic approach to constructing numerical approximations that can be incorporated into a wide variety of Partial differential equations (PDE) and/or Ordinary differential equations (ODE) solvers. This paper presents a framework of the nonlinear finite element based on HiDeNN approximation (nonlinear HiDeNN-FEM). This is enabled by three basic building blocks employing structured deep neural networks: 1) A partial derivative operator block that performs the differentiation of the shape functions with respect to the element coordinates, 2) An r-adaptivity block that improves the local and global convergence properties and 3) A materials derivative block that evaluates the material derivatives of the shape function. While these building blocks can be applied to any element, specific implementations are presented in 1D and 2D to illustrate the application of the deep learning neural network. Two-step optimization schemes are further developed to allow for the capabilities of r-adaptivity and easy integration with any existing FE solver. Numerical examples of 2D and 3D demonstrate that the proposed nonlinear HiDeNN-FEM with r-adaptivity provides much higher accuracy than regular FEM. It also significantly reduces element distortion and suppresses the hourglass mode.

Failure of levees induced by toe uplift: Investigation of post-failure behavior using material point method

Levees are essential structures in flood defense systems, and their failures can lead to devastating consequences on the surrounding territories. One of the failure mechanisms mostly controlled by the foundation soil stratigraphy is the instability of the land side slope, triggered by the development of high uplift pressures in the foundation. This complex phenomenon has been investigated experimentally with centrifuge tests or large-scale tests and numerically with the limit equilibrium method (LEM) and the finite element method (FEM). In this work, we applied a multiphase formulation of the material point method (MPM) to analyze the development of toe uplift instability mechanism, from the onset of failure to large displacements. The numerical model is inspired by an experiment carried out in a geotechnical centrifuge test by Allersma and Rohe (2003). The comparison with the experiment allows for understanding critical pore pressure triggering large displacements in the foundation soils. Moreover, we numerically evaluated the impact of different values of foundation soils' hydraulic conductivity on the failure mechanism. The results show that hydraulic conductivity mainly influences the time of failure onset and the extension of shear localization at depth. Finally, the advantages of using large displacement approaches in the safety assessment of earth structures are discussed. Unlike FEM, there are no issues with element distortions generating difficulties with numerical convergence, allowing for full post-failure reproduction. This capability permits precise quantification of earth structure damages and post-failure displacements. The ensuing reinforcement systems' design is no longer over-conservative, with a significant reduction in associated costs. ©2022 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

The Combined Bearing Capacities of Anchor Chain Segment by Considering Its Actual Geometry and Roughness

The soil resistances along the embedded ground chain affect the pull-out capacity of anchor as they determine the magnitude and direction of tension at the padeye. To facilitate analyses, the chain was usually simplified as a cylindrical line. The chain segment with actual geometry, buried deeply in clayey soil, is studied using a large deformation finite element approach to overcome severe distortion of soil elements around the chain. The uniaxial resistances obtained by the large deformation analyses are verified by comparison with the existing model tests and simplified solutions, followed by presentation of the yield envelope against combined loading. Both the probe test and swipe test are used to form the yield envelopes, and their results have good consistency. The influence of roughness of chain–soil interface on the soil resistances is quantified as well. It is found that the envelope of the chain segment with actual geometry is smaller than that against the simplified cylindrical shape; therefore, the most convenient design may not be the safest option.

Suppression of thermally induced lensing in composite disk active elements by shaping a heat-removing plate

We propose an original method of suppressing thermally induced beam distortions in composite active elements of disk geometry. The main idea of the method is to use a heatsink of special geometry to provide heat removal from the active element only in the pump area. In this way, the heat flows and temperature gradients in the thick active element, and, as a consequence, thermally induced distortions are reduced. The wavefront distortions, temperature, and gain in the composite element mounted in a profiled heatsink have been simulated numerically and measured in experiment. A 2.5-fold reduction of thermally induced lensing compared to a flat heatsink was demonstrated in the experiment at the same small signal gain.

Simulation of Cold-Formed Steel Shear Wall Sheathed with Steel Plate: Non-Linear Finite Element Modelling and Analysis

The usage of cold-formed steel (CFS) is gaining popularity all around the world these days. Buildings made of such elements as an independent structural system are applied in the construction of small commercial complexes, low-raised buildings, industrial units, and single-story sports halls. CFS shear walls sheathed with steel sheets are the most popular lateral-load resisting system in low to mid-raised structures. In this paper, a full-scale steel seated CFS shear wall has been simulated by a non-linear finite element method. Furthermore, parametric studies have been carried out to analyze the effects of the blocking members, fastener spacing at steel plate to boundary frame connections, and steel sheet thickness on the behavior of CFS shear wall sheathed with steel plate. It was concluded that the blocking members prevent the studs from twisting and decrease the local bucking of the studs. Meanwhile, the results indicate that the thickness of the steel plate affects the shear strength of the CFS shear wall system to an extent. Besides, increasing the spacing of the fasteners at the connection of the steel plate to the frame system affects the buckling mode of the steel plate, and by increasing the spacing of the fasteners from 100 mm to 150 mm and 200 mm the nominal shear strength of the wall system decreased by 6.5% and 14.1% respectively, while decreasing the fastener spacing causes web distortion of the boundary column elements.

Experimental investigation on structural response of multi-story buildings subjected to differential settlement of its foundations

PurposeThis article aims to address an outstanding problem dealing with the structure of multi-story buildings subjected to differential settlement of the building's foundation.Design/methodology/approachDifferential settlement between foundation units of multi-story structures has been responsible for causing damage to buildings and often catastrophic failure and loss of life. The dynamic changes in the loading conditions of the structure and the changes in the underlying ground due to environmental changes are causing this undesirable differential settlement, which is manifested in the form of additional stresses in beams, columns and distortion of the structure elements. This study presents the results of an experimental investigation on a prototype model of a multi-story building subjected to differential settlement of the building's foundation. The model is a four-floor aluminum structure, instrumented to measure the stresses induced in the structure elements due to the settlement of a center, edge and corner column, respectively, which represent the critical conditions of the structure.FindingsThe experimental results of this study can be used as a guideline for the design of structures.Originality/valueThe current study is the original research developed by the authors.

A high-precision formula for mixed-order polygon elements based on SBFEM

A satisfactory balance between solution precision and computational efficiency can be achieved via mixed-order elements, however, the generality and robustness of commonly used methods can be further optimized. In this paper, a flexible and versatile mixed-order analysis method is developed based on Scaled Boundary Finite Element Method (SBFEM) theory, wherein one-dimensional linear and quadratic functions are combined to interpolate circular boundaries. The applicability and accuracy of the proposed method for different problems are explored and compared, and good accuracy and tolerance of element distortion performance are revealed. Moreover, compared with the quadratic element, computational efforts can be reduced considerably, enabling efficiency to be enhanced. Additionally, a polygon mixed-order formula can be directly derived, benefiting from the advantages of the SBFEM, wherein stronger universalities are rendered. In summary, the proposed method improves the flexibility and robustness of the mixed-order cells, and distinctive superiorities are revealed, providing an alternative option for the efficient and high-precision numerical analysis of vital structures.