Narrow Results

This research is concerned with the thermal bending and stability of temperature-dependent nanocomposite curved pipes strengthened with carbon nanotubes (CNTs) subjected to uniform temperature rise. Thermo-mechanical characteristics of the polymer composite pipe are assumed to vary entirely in the thickness by a non-uniform function of the radius. Five different patterns are selected to model the propagation profile of CNTs amongst the pipe thickness. Based on the shear deformation and von-Karman kinematic hypothesis, nonlinear balance equations of the polymer curved pipe are determined via varying the total potential energy of the system. Governing equations as a set of coupled nonlinear differential equations are analytically solved using a perturbation-based technique. Closed-form solutions are derived to estimate large-amplitude deflection of nanocomposite curved pipes with pinned and clamped boundaries under uniform thermal loading. The obtained results show the influences of important parameters such as material/geometrical characteristics and foundation stiffness on the thermally induced nonlinear response of polymer nanocomposite curved pipes.

The dynamic damage evolution for PP/PA blends with different compatibilizers is studied in high strain rates from two different approaches, namely by determining the unloading elastic modulus of specimen experienced impact deformation and by combining the split Hopkinson pressure bar (SHPB) experimental technique with the back-propagation (BP) neural network. The results obtained by both approaches consistently show that a threshold strain ε_th exists for dynamic damage evolution, and both the damage evolution and ε_th are dependent on strain and strain rate. For non-linear visco-elastic materials, the damage evolution determined by the unloading elastic modulus provides an underestimation of real damage evolution.

Conventional finite element (FE) analysis of bulk metal forming processes often breaks down due to severe mesh distortion. In recent years, meshless methods have been considerably developed for structural applications. The main feature of these methods is that the problem domain is represented by a set of nodes, and a finite element mesh is unnecessary. This new generation of computational methods can avoid time-consuming meshing and remeshing. A meshless method based on reproducing kernel particle method (RKPM) is applied to bulk metal forming analysis. The displacement shape functions are developed from a reproducing kernel (RK) approximation that satisfies consistency conditions. The shape function is modified to impose essential boundary conditions accurately and expediently. A material kernel function that deforms with the material is introduced to assure the stability of the RKPM shape function during large deformations. A program based on RKPM is developed to simulate two examples of bulk metal forming process such as ring compression and cold upsetting, and numerical results demonstrate the performance of the meshless method in bulk metal forming analysis.

In this paper, we review recent developments that aim to achieve further understanding of the structure of atomic nuclei, by capitalizing on exact symmetries as well as approximate symmetries found to dominate low-lying nuclear states. The findings confirm the essential role played by the Sp(3, ℝ) symplectic symmetry to inform the interaction and the relevant model spaces in nuclear modeling. The significance of the Sp(3, ℝ) symmetry for a description of a quantum system of strongly interacting particles naturally emerges from the physical relevance of its generators, which directly relate to particle momentum and position coordinates, and represent important observables, such as, the many-particle kinetic energy, the monopole operator, the quadrupole moment and the angular momentum. We show that it is imperative that shell-model spaces be expanded well beyond the current limits to accommodate particle excitations that appear critical to enhanced collectivity in heavier systems and to highly-deformed spatial structures, exemplified by the second 0⁺ state in ¹²C (the challenging Hoyle state) and ⁸Be. While such states are presently inaccessible by large-scale no-core shell models, symmetry-based considerations are found to be essential.

The property of free movement of particles allows for most meshless particle methods to be efficiently used for simulation of solid problems involving large deformation as it removes the necessity of remeshing, which is one of the time-consuming parts of the traditional finite element method based on an updated Lagrangian formulation. One of the main sources of instabilities in meshfree particle methods, which approximate the strong form of partial differential equations, is the existence of extra high frequency vibrations. They are induced into the solution due to the use of truncated Taylor series expansions. The cumulative effect of the extra vibrations makes the solution to be polluted by zero energy modes and tensile instabilities. In this paper, the CSPM particle method is used to solve elastodynamic large deformation problems based on an updated Lagrangian procedure. A field smoothing approach, recently proposed for reduction of instabilities that rise from excessive high frequency vibrations, is further extended to large deformation problems. Also, the phenomenon of particles penetration can be prevented without the requirement of any additional artificial damping forces. Another major advantage of the new approach is its generality which allows for its implementation into other particle methods and its application for solving other physical problems. A variety of large deformation problems are solved by the proposed approach and the results are compared with other available results.

This investigation uses the absolute nodal coordinate formulation (ANCF) method to solve statics and dynamics of microbeams for the first time. A comprehensive model for the investigation of statics and dynamics of microbeams by using gradient deficient elements of the ANCF and modified couple stress theory (MCST) is developed. The vibration equations of a planar hub-microbeam system with constant angular rotations are derived considering the static equilibrium. Accuracy of the ANCF method for microbeams is demonstrated. Large deformation problems of cantilever microbeams are solved and the influences of material length scale on beam deformation are studied. When the beam thickness becomes smaller, the deflection of the microbeam calculated by the current model is smaller, and the size effect becomes more significant. The size effect only has influence on the bending vibration of the microbeam. The variations of the angular speed as well as the scale parameter can trigger frequency veering phenomena. The present work could be used in dynamic or vibration predictions for microelectromechanical systems (MEMS) with both large displacements and large deformations.

In this paper, by implanting the rigid body rule (RBR)-based strategy for static nonlinear problems into the implicit direct integration procedure, an efficient and robustness nonlinear dynamic analysis method for the response of framed structures with large deflections and rotations is proposed. The implicit integration method proposed by Newmark is improved by inserting an intermediate time into the time step and by adding the 3-point backward difference in the second substep so as to preserve the momentum conservation and to maintain the stability of the direct integration method. To solve the equivalent incremental equations of motion, the RBR is built in to deal with the rigid rotations and the resulting additional nodal forces of element. During the increment-iterative procedure, the use of RBR-qualified geometric stiffness in the predictor reduces the numbers of iterations, while the elastic stiffness alone in the corrector to update the element nodal forces makes the computation efficiency and convergence with no virtual forces caused by the ill geometric stiffness. The proposed algorithm is advanced in the applications of several framed structures with highly nonlinear behavior in the dynamic response by its simplicity, efficient and robustness.

This paper introduces a new rigid finite element method (RFEM) formulation for dynamic analysis of plates. In RFEM, a flexible body is divided into several rigid elements which are interconnected by spring and damping elements. Mainly, RFEM has been used to model systems with beam-like slender components, such as ropes and cables, and few RFEM formulations were developed to model plates and shells. In this study however, by means of the Timoshenko beam theory and cuboid rigid elements, a novel RFEM formulation is developed to model flexible flat plates with generic geometries of the surface, considering large deformation. For this purpose, an RFEM formulation is presented for straight beams with rectangular cross-section by means of the Timoshenko beam theory. Next, this formulation is expanded to model flexible rectangular plates with uniform thickness and then, it is elaborated on how to model non-rectangular plates with uniform thickness using only cuboid elements and consequently, the development of the proposed RFEM formulation is completed. After investigating various case studies, the competence of the proposed formulation is evaluated thoroughly. The results of RFEM came on a proper agreement with the FEM results in a way that the maximum difference between these results in dynamic analysis was about 3%.

Flexible lightweight arched structures are finding increasing use as components in smart engineering applications. Such structures are prone to various types of instability under moving transverse loads. Here, we study deformation and vibration of a hinged circular arch under a uniformly moving point load using geometrically-exact rod theory to allow for large pre- and post-buckling deformations. We first consider the quasi-statics problem, without inertia. We find that for arches with relatively large opening angle ($\sim$160${}^{\circ }$) a sufficiently large traversing load will induce an out-of-plane flopping instability, instead of the in-plane collapse (snap-through) that dominates failure of arches with smaller opening angle. In a subsequent dynamics study, with full account of inertia, we then explore the effect of the speed of the load on this lateral buckling. We find speed to have a delaying (or even suppressing) effect on the onset of three-dimensional bending–torsional vibrations and instability. Based on numerical computations we propose a power law describing this effect. Our results highlight the role of inertia in the onset of elastic instability.

Here we investigate the kinetic model for the large deformation theory of hydrogel under the outside stimulations. We present the large deformation dynamical model in the following two points. (1) The phase transition caused by the deformation gradient is concerned, which makes the model more integral. (2) Based on the steady-state model, the time-dependent large deformation model is proposed and the time developing process is investigated. Considering the force of the large deformation, we introduce the heat equation to express the transformation of the chemical potential. The extended model can be used to describe the development of the large deformation. We present numerical examples of the cylindrical hydrogel for one- and two-dimensional cases under pressure and stretch. Besides, some key parameters are studied to test the model.

A finite element contact approach based on the Moving Friction Cone (MFC) formulation is presented herein. The formulation is based on the contact constraint described using a single gap vector. Such a simplification, in comparison with the standard approach where normal and tangential gap vectors are used, results in significantly simpler, shorter and faster element code. The associated penalty is formulated to include large deformations and displacements. Within this approach a triangular contact element is developed using a high abstract mathematical level of symbolic description. Using this technique, a consistent linearization is obtained which leads to quadratic rates of convergence. Furthermore, the new technique results in algorithmic robustness, fast evaluation time, as well as a compact element code.

In many cases, it is advantageous to discretize a domain using several finite element meshes instead of a single mesh. For example, in fluid-structure interaction problems, an Eulerian mesh is advantageous for the fluid domain while a Lagrangian mesh is most suited for the structure. However, the interface conditions between different types of meshes often lead to significant errors. A method of treating different meshes by smoothly varying the description from Lagrangian to Eulerian in an interface or blending domain is presented. A Lagrangian mesh is used for the structure while two different types of mesh are used for the fluid. Arbitrary Lagrangian-Eulerian (ALE) meshes are used in the regions of the fluid-structure interfaces while Eulerian meshes are used for the remainder of the fluid domain. A blending function is used to couple the ALE and Eulerian meshes to ensure a smooth transition from one mesh to another. The method is tested on two fluid-structure problems — flow past a hinged plate, and fluid expansion in a closed container. Results are in good agreement with standard finite element and analytical solutions.

In the modeling and simulation of microelectromechanical system (MEMS) devices, such as the microswitch, the large deformation or the geometrical nonlinearity should be considered. Due to the issue of mesh distortion, the finite element method (FEM) is not effective for this large deformation analysis. In this paper, a local meshfree formulation is developed for geometrically nonlinear analysis of MEMS devices. The moving least squares approximation (MLSA) is employed to construct the meshfree shape functions based on the arbitrarily distributed field nodes and the spline weight function. The discrete system of equations for two-dimensional MEMS analysis is obtained using the weighted local weak form, and based on the total Lagrangian (TL) approach, which refers all variables to the initial configuration. The Newton–Raphson iteration technique is used to get the final results. Several typical microswitches are simulated by the developed nonlinear local meshfree method. Some important parameters of these microswitches, e.g. the pull-in voltage, are studied. Compared with the experimental results and results obtained by linear analysis, nonlinear meshfree analysis of microswitches is accurate and efficient. It has demonstrated that the present nonlinear local meshfree formulation is very effective for geometrically nonlinear analysis of MEMS devices, because it totally avoids the issue of mesh distortion in the FEM.

The smoothed finite element method (SFEM) was developed in order to eliminate certain shortcomings of the finite element method (FEM). SFEM enjoys some of the flexibilities of meshfree methods. One advantage of SFEM is its applicability to modeling large deformations. Due to the absence of volume integration and parametric mapping, issues such as negative volumes and singular Jacobi matrix do not occur. However, despite these advantages, SFEM has never been applied to problems with extreme large deformation. For the first time, we apply SFEM to extreme large deformations. For two numerical problems, we demonstrate the advantages of SFEM over FEM. We also show that SFEM can compete with the flexibility of meshfree methods.

This paper presents a new particle formulation for extreme material flow analyses in the bulk forming applications. The new formulation is first established by an introduction of a smoothed displacement field to the standard Galerkin formulation to eliminate zero-energy modes in conventional particle methods. The discretized system of linear equations is consistently derived and integrated using a direct nodal integration scheme. The linear formulation is next extended to the large deformation quasi-static analysis of inelastic materials. As quasi-static Lagrangian simulation proceeds in the severe deformation range, the analysis method is switched to explicit dynamics formulation and an adaptive Lagrangian kernel approach is preformed to reset the reference configuration and maintain the injective deformation mapping at the particles. Both nonconvex and convex meshfree approximations are investigated in this study. Several numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed method.

A new type of smoothed finite element method (S-FEM), F-barES-FEM-T4, is demonstrated in static large deformation elastoplastic cases. F-barES-FEM-T4 combines the edge-based S-FEM (ES-FEM) and the node-based S-FEM (NS-FEM) for 4-node tetrahedral (T4) elements with the aid of the F-bar method in order to resolve the major issues of Selective ES/NS-FEM-T4. As well as most of the other S-FEMs, F-barES-FEM-T4 inherits pure displacement-based formulation and thus has no increase in DOF. Moreover, the cyclic smoothing procedure introduced in F-barES-FEM-T4 is effective to adjust the smoothing level so that pressure checkerboarding (oscillation) is suppressed reasonably. Some examples of static large deformation analyses for elastoplastic materials proof the excellent performance of F-barES-FEM-T4 in contrast to the conventional hybrid T4 element formulation.

A state-of-the-art tetrahedral smoothed finite element method, F-barES-FEM-T4, is demonstrated on viscoelastic large deformation problems. The stress relaxation of viscoelastic materials brings near incompressibility when the long-term Poisson’s ratio is close to 0.5. The conventional hybrid 4-node tetrahedral (T4) elements cannot avoid the shear locking and pressure checkerboarding issues, meanwhile F-barES-FEM-T4 can suppress these issues successfully by adopting the edge-based smoothed finite element method (ES-FEM) with the aid of the F-bar method and the cyclic smoothing procedure. A few examples of analyses verify that F-barES-FEM-T4 is locking-free and pressure oscillation-free in viscoelastic analyses as well as in nearly incompressible hyperelastic or elastoplastic analyses.

In this work, a three-dimensional (3D) nonlinear smoothed finite element method (S-FEM) solver is developed for large deformation problems. Node-based and face-based S-FEM using automatically generable four-noded tetrahedral elements (NS-FEM-Te4 and FS-FEM-Te4) are adopted to find the solution bounds in strain energy. The lower bound solutions are obtained using FEM-Te4 and FS-FEM-Te4, while the upper bound solutions are obtained using NS-FEM-Te4. A combined $\alpha$S-FEM-Te4 with a scaling factor $\alpha$ that controls the combination is constructed to find nearly exact solutions for the nonlinear solids mechanics problems through adjusting $\alpha$. This is achieved using the property that a successive change of scaling factor $\alpha$ can make the model transform from “overly-stiff” to “overly-soft”. Considering the properties of FS-FEM and NS-FEM, a selective FS/NS-FEM-TE4 is also used to solve 3D nonlinear large deformation problems, which produces a lower bound in strain energy. Hyperelastic Mooney–Rivlin and Ogden materials are both used in this study. Numerical examples reveal that S-FEM-Te4 is an effective method for obtaining solution bounds together with the standard FEM, and the FS-FEM-Te4, NS-FEM-Te4 and selective FS/NS-FEM-TE4 are robust with the high accuracy and computational efficiency for large deformation nonlinear problems.

A new concept of smoothed finite element method (S-FEM) using 10-node tetrahedral (T10) elements, CS-FEM-T10, is proposed. CS-FEM-T10 is a kind of cell-based S-FEM (CS-FEM) and thus it smooths the strain only within each T10 element. Unlike the other types of S-FEMs [node-based S-FEM (NS-FEM), edge-based S-FEM (ES-FEM), and face-based S-FEM (FS-FEM)], CS-FEM can be implemented in general finite element (FE) codes as a piece of the element library. Therefore, CS-FEM-T10 is also compatible with general FE codes as a T10 element. A concrete example of CS-FEM-T10 named SelectiveCS-FEM-T10 is introduced for large deformation problems of nearly incompressible solids. SelectiveCS-FEM-T10 subdivides each T10 element into 12 four-node tetrahedral (T4) subelements with an additional dummy node at the element center. Two types of strain smoothing are conducted for the deviatoric and hydrostatic stress evaluations and the selective reduced integration (SRI) technique is utilized for the stress integration. As a result, SelectiveCS-FEM-T10 avoids the shear/volumetric locking, pressure checkerboarding, and reaction force oscillation in nearly incompressible solids. In addition, SelectiveCS-FEM-T10 has a relatively long-lasting property in large deformation problems. A few examples of large deformation analyses of a hyperelastic material confirm the good accuracy and robustness of SelectiveCS-FEM-T10. Moreover, an implementation of SelectiveCS-FEM-T10 in the FE code ABAQUS as a user-defined element (UEL) is conducted and its capability is discussed.

A locking-free face-based S-FEM, combined with the Averaging Nodal Pressure (ANP) technique, is proposed to solve explicit dynamics of geometric nonlinear nearly-incompressible solids, using simplest linear tetrahedral elements (FS-FEM/ANP-T4). An explicit Adaptive Dynamic Relaxation (ADR) technique is also implemented for the analysis of quasi-static problems. Our studies have found that the proposed method has better accuracy and convergence compared to the standard FEM with ANP (FEM/ANP) and previous selective face-based and Node-based S-FEM (FS/NS-FEM). With the ADR, proposed method can reach the nonlinear quasi-static response much faster than the conventional explicit dynamic relaxation. No temporal instability is observed in FS-FEM/ANP-T4 in large deformation case. In addition, FS-FEM/ANP-T4 also equips the robustness against mesh distortion as FS/NS-FEM but uses less computational time. It has also been applied to solve a practical 3D problem, a rubber hanger for the car exhaust system. FS-FEM/ANP-T4 can be considered as an excellent numerical method other than FS/NS-FEM for simulating rubber-like materials.