Thin Plate Element Research Articles

Nonlinear Dynamics Research of Ground Undulatory Fin Robot with Flexible Deformation and Frictional Contact.

The unique rigid-flex connection between the fin-rays and fin-surface in a bionic undulatory fin robot endows the fin-surface with both active flexibility and load-bearing capacity, enabling this robot to perform amphibious motions in underwater, terrestrial, and even marshy environments. However, investigations into dynamic modeling problems for the undulatory fin robot, considering the impact of nonlinear deformation and frictional contact on ground locomotion performance, are scarce. Given this, based on the absolute nodal coordinate formulation (ANCF), this paper presents an efficient and accurate nonlinear dynamic model for this robot to elucidate the fin's flexible deformation and motion law. This model considers material, geometric, and boundary nonlinearities, utilizing ANCF thin plate elements and reference nodes to individually describe the fin-surface and fin-rays of the undulatory fin. Then, by using the master-slave technique, a frictional contact formulation for the fin and the ground is proposed. Furthermore, we conduct in-depth research and analysis on the formation and undulatory motion of the undulatory fin, encompassing its static deformation, static contact deformation, and frictional contact motion, and successfully obtain its responses under various conditions. Research indicates that during fin-surface motion, longitudinal sliding or a tendency for sliding at the contact points results in the undulatory fin moving in a crawling gait. The proposed theoretical model correctly captures the fin's complex nonlinear deformations and frictional characteristics and reveals its ground locomotion mechanism, whose effectiveness and superiority are validated through numerical examples and experiments.

Transverse free vibration analysis of thin sectorial plates by the weak form quadrature element method

The weak form quadrature element method is applied to free vibration analysis of thin sectorial plates with arbitrary vertex angles and boundary conditions. To tackle the strong stress singularity around the vertex, analytical displacement descriptions are introduced into the inner sectorial subdomain, while the outer annular subdomain is modeled by a single weak form quadrature thin plate element. The continuity on the interface between the two subdomains is enforced afterwards. Eventually, a generalized eigenvalue formulation is established after introducing Hamilton’s principle. The first six non-dimensional frequency parameters for various vertex angles and boundary conditions are obtained and compared with available results. Several typical free vibration modes are plotted. The accuracy, convergence rate, and computational cost of the present formulation are discussed at length.

Three new triangular thick plate/shell elements based on absolute nodal coordinate formulation

In this paper, three new triangular fully parameterized thick plate/shell elements are proposed based on the absolute nodal coordinate formulation. The volume parameters and corresponding independent volume gradient vectors are used to simplify the element construction. The node-wise structural parameter is adopted to circumvent the slope discontinuity issue associated with the volume gradient vectors. Two three-node elements inherit the interpolation strategy in the membrane direction of a well verified thin plate element. For the thickness direction, linear and quadratic interpolation are used in the three-node elements. Inspired by the quadrilateral plate elements with gradient vectors only along thickness direction, a six-node triangular element is presented with quadratic interpolation in both membrane and thickness direction. Three static analyses with large deformation and one dynamic analysis are conducted to evaluate the performance of the new elements. It concludes that the three-node element with linear interpolation in the thickness direction performs not well due to the incompatible/low interpolation in the thickness direction. The other two elements show good accuracy in all the numerical tests. Though the six-node element exhibits slightly higher accuracy than the quadratic three-node element, its DOFs are much more than the quadratic three-node element, which makes it less attractive.

High-fidelity modeling of dynamic origami folding using Absolute Nodal Coordinate Formulation (ANCF)

Origami has evolved into a framework for creating engineering systems at vastly different scales: from large deployable airframes to architected materials to small DNA machines. These emerging applications require us to develop high-fidelity models that can simulate and examine folding-induced mechanical responses, especially those involving significant facet rotation, non-uniform deformation, and complex dynamics. To this end, this study formulates and experimentally validates a new origami mechanics model based on Absolute Nodal Coordinate Formulation (ANCF), which has unique advantages for predicting the nonlinear dynamics of multibody systems with large rotation and deformation. This new model treats origami facets as ANCF thin plate elements rotating around compliant creases. Moreover, Torsional Spring Damper Actuator (TSDA) connectors are developed to represent crease folding. After careful calibration with experimentally measured constitutive material properties, this study provides the first reported quantitative agreement between simulation predictions and experiment results involving complex and non-uniform facet deformation and transient dynamic responses. Therefore, this model can help deepen our knowledge of folding-induced mechanics and dynamics, fostering future applications for origami.

Accurate dynamic modeling of detumbling rotating satellites with large flexible solar panels

Stabilizing a malfunctioning satellite to a low rotating speed is required to ensure safe capture. The detumbling method based on a flexible contactor is efficient and safe due to its relatively large operating force and soft contact. However, flexible components of the target such as the long solar panel will deform large under this intense external force, which makes accurate modeling and analysis of the detumbling process particularly challenging. In this paper, the dynamic problem of detumbling a rotating satellite with large-deformation solar panels is first studied. The target satellite is accurately modeled via global frame approaches, where the new visco-elastic thin plate element of the absolute nodal coordinate formulation is proposed to describe the solar panels. Then the contact model is built based on the geometric relation between the flexible contactor and the solar panel. Finally, dynamic performances during detumbling are compared between flexible and rigid targets, and the detumbling process of the highly flexible satellite is analyzed. All simulation results show that the flexibility of the target should be considered carefully in contact detumbling tasks.

Functionalising buckling for structural morphing in kinetic façades: Concepts, strategies and applications

Functional structures can be designed to adapt to changing external environmental conditions by suitable shape morphing. In recent years, the instability of structural components such as the buckling of thin plate elements has emerged as a viable solution for structural shape morphing, leading to increasing research attention. In this context, the intrinsic features of buckling including the high rate of motion and sudden release of energy are harnessed for structural functionality. The attention to buckling is motivated by the ubiquitous requirement in the construction industry to design buildings with increasingly low energy consumption. The well-known concept of zero energy buildings utilises adaptive shading and natural ventilation as passive energy systems, for which shape morphing by buckling is particularly effective. Façades, being the primary constituent of the building envelope, are crucially important for enhancing energy efficiency and indoor comfort. In this study, we explore the potential of utilising structural instability to develop shape morphing mechanisms that can be integrated into building facades for desired functionality. A series of novel concept ideas and systems are proposed in which the instability of structural elements is configured to produce the desired function. The proposed ideas are subsequently simulated using finite element analyses to validate the feasibility and effectiveness of utilising buckling as a reliable mechanism in kinetic façade control. It is shown that the systems can be integrated into autonomous building modules by using sensor-initiated smart materials such as shape memory alloys for actuation.

Diffractive optical system design by cascaded propagation.

Modern design of complex optical systems relies heavily on computational tools. These frequently use geometrical optics as well as Fourier optics. Fourier optics is typically used for designing thin diffractive elements, placed in the system's aperture, generating a shift-invariant Point Spread Function (PSF). A major bottleneck in applying Fourier Optics in many cases of interest, e.g. when dealing with multiple, or out-of-aperture elements, comes from numerical complexity. In this work, we propose and implement an efficient and differentiable propagation model based on the Collins integral, which enables the optimization of diffractive optical systems with unprecedented design freedom using backpropagation. We demonstrate the applicability of our method, numerically and experimentally, by engineering shift-variant PSFs via thin plate elements placed in arbitrary planes inside complex imaging systems, performing cascaded optimization of multiple planes, and designing optimal machine-vision systems by deep learning.

A rotation-free quadrature element formulation for free vibration analysis of thin sectorial plates with arbitrary boundary supports

Due to corner stress singularities, free vibration analysis of thin sectorial plates with arbitrary boundary supports including a free vertex is a rather challenging problem. In this paper, a novel rotation-free quadrature element formulation based on Kirchhoff plate theory is presented to solve the problem. Different from all existing quadrature thin plate element formulations, rotational degrees of freedom are not used. Instead, a boundary point is modeled by two nodes separated by a very small distance and thus the C1 continuity is easily enforced. Explicit formulations with arbitrary number of nodes and nodes of any type are worked out to ease the p-refinement. Numerical results demonstrate that the proposed formulation is simple, straightforward and has excellent performance for solving thin sectorial plate with arbitrary combinations of boundary supports. Some tabulated data are believed new which may serve as a reference.

The polygonal scaled boundary thin plate element based on the discrete Kirchhoff theory

The scaled boundary finite element method (SBFEM) is a powerful method for solving elastostatics problems based on polygonal elements. In this paper, we firstly construct the quadratic polygonal scaled boundary element only depends on the boundary nodal displacements by transforming the additional degrees of freedom derived from the constant body loads to those by the boundary nodes. Further, combining with the discrete Kirchhoff theory, we construct the polygonal scaled boundary thin plate element, which can possess the second order completeness. The element stiffness matrix for the thin plate problem can be transformed by the stiffness matrix for the plane problem directly by avoiding to compute the shape functions of SBFEM. Numerical examples verify that the proposed polygonal scaled boundary thin plate element has good accuracy.

Post-impact flexural capacity of UHPFRC plates

This work aims to demonstrate the effective use of fibre reinforcement in thin plate elements made of UHPFRC under projectile impact loading. The use of fibre reinforcement is very efficient in case of ballistic loading, as fibres are evenly distributed over the entire volume of the material body and possible damage to the plate is thus suppressed in all points of the plate element equally. The aim of this study is therefore to provide data on the residual flexural capacity of plates that have been significantly damaged by the impact of the projectile and to demonstrate the benefits of using fibre reinforcement for localized impact loading.

Stability analysis of thin-walled composite plate in unsymmetrical configuration subjected to axial load

The subject of the study were thin plate elements with a central cut-out of regular shapes, made of carbon-epoxy composite, subjected to uniform compression. The purpose of the analysis was the possibility of using such elements as elastic elements, which stiffness can be designed by changing the geometric parameters of the cut-out and by the appropriate configuration of the composite layers layout. To ensure the stable work of the structure in the postcritical range, in the plate construction an unsymmetrical composite layer layout was used, having selected B matrix couplings, described in i.a. by York and Altenbach. For the adopted solution, a numerical analysis of the structure using the finite element method was carried out. The scope of numerical simulations included linear analysis of eigen problem and calculations using geometrically non-linear procedures. The numerical tool used in research was the ABAQUS® program. Experimental studies were carried out on an universal testing machine using the optical ARAMIS system. The purpose of the calculations was to select the laminate layer layout ensuring the lowest flexural-torsional buckling form, ensuring stable work of the structure in the postcritical range.

Topology optimization for removing internal resonances of a rotating thin plate

Internal resonance allows energy to transfer between eigenmodes and sometimes results in undesirable phenomena. Topology optimization has the ability to control the eigenfrequencies of a structure and is therefore possible to remove the internal resonances. In this study, topology optimization is studied for removing internal resonances of a rotating rectangular thin plate. First of all, an accurate dynamic model is established for the rotating thin plate by considering the Coriolis force. The thin plate element of the absolute nodal coordinate formulation (ANCF) is used to discretize the rotating thin plate and establish the dynamic equation. When the dynamic equation is transformed from the absolute frame to the rotating frame for modal analysis, the Coriolis force term shows up and is analytically derived. Then, an explicit and efficient topology optimization method, i.e., the method of moving morphable components (MMC) is employed to optimize the rotating thin plate. In order to remove the internal resonances, the detuning parameters are defined so that removing the internal resonances is equivalent to maximizing the minimum absolute detuning parameter. The corresponding max-min optimization problem can be dealt with via a bound formulation. Finally, three numerical examples are presented to validate the dynamic model and the topology optimization methodology. Two objectives are considered for optimization, i.e., removing the internal resonances of the rotating thin plate at different specific angular speeds and removing the most common 1:1 or 1:2 internal resonances of the rotating thin plate during a certain range of angular speeds.

The polygonal spline thin plate element based on the discrete Kirchhoff theory

As we know, the polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Besides, the hanging nodes can be handled as irregular nodes of polygonal element. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. However, the research on polygonal plate element is lack. The difficulty of polygonal element is the construction of the interpolation bases.In this paper, by using the spline and B-net method, we construct a polygonal spline thin plate element based on the discrete Kirchhoff theory. The key is to construct a set of spline interpolation bases corresponding to the boundary nodes of the polygonal element including the irregular case. The basic idea is to subdivide the $n$-sided polygon into $n$ subtriangles. We represent the spline functions in each subtriangle as quadratic polynomials in the B-net form. Then the degree of freedoms of the B-net coefficients corresponding to the interior B-net domain points are eliminated by some proper continuous conditions. As a result, we obtain the spline interpolation bases as the shape functions on the polygonal element. Combined with the discrete Kirchhoff theory, the new polygonal thin plate element is constructed and denoted by DKPS element. The nodal degrees of freedom are the displacement and two rotations at each vertex of the polygonal element. It can possess quadratic completeness in the Cartesian coordinates and is valid for both nonconvex and irregular polygonal elements. The mathematical formulas for the element stiffness matrices are also presented, which can be computed directly by the B-net coefficients of the spline bases. Thus there is no need to use the numerical integration in the computation of the element stiffness matrices. Some numerical experiments show that the new element has efficiency and good accuracy even for some badly distorted meshes.

The Rigid-Flexible-Thermal Coupled Analysis for Spacecraft Carrying Large-Aperture Paraboloid Antenna

Abstract Since the thermal load would adversely introduce degradation to the normal operation of spacecraft, resulting in unpredictable thermal-dynamic behavior, thermomechanical coupling problems are important and have been investigated extensively. Based on the absolute nodal coordinate formulation (ANCF), a thermal integrated ANCF thin plate element based on the unified description is constructed, which could depict the displacement and the temperature field integratedly. By means of the proposed element, the heat transfer and continuum mechanics are integrated in the unified finite element method (FEM) mesh of revolving paraboloid antenna. Additionally, the ANCF reference node is introduced for describing the rigid central hub where the antenna is mounted on to make the rigid-flexible-thermal coupled response being captured in a unified analysis procedure. The solar radiation input and the surface emitting radiation are included in the heat transfer equations. Furthermore, the influence of the rigid body motion and the deformation on the radiant absorption are also considered with the self-shadowing. The established rigid-flexible-thermal coupled simulation is performed on a modified generalized-α integrator which solves the set of multidisciplinary governing equations synchronously. For revealing the nonlinear behavior of the rigid-flexible-thermal coupled system, the observed thermally induced vibration and perturbation on the pointing accuracy of the spacecraft are given in the results, and the feasibility of the presented method is proved.

Coupling relationship of the non-ideal parallel mechanism using modified Craig-Bampton method

The coupling relationship in the dynamics model of 4-SPS/PS (P-prismatic joint, S-spherical joint) parallel mechanism with a flexible moving platform and clearance spherical joint is investigated. Two primary coupling relationships are studied: (i) the coupling between reference motion and elastic deformation; (ii) the coupling between the elastic vibration and collision. Firstly, the dynamic model of the flexible moving platform is formulated using the floating frame of reference (FFR) formulation. According to the topology of this parallel mechanism, the fixed-fixed reference conditions are selected and imposed at the finite element (FE) analysis stage for the thin-plate element. Also, considering that the conventional Craig-Bampton (CB) method does not impose any reference condition at FE analysis stage, therefore, a modified CB method is proposed to obtain the fixed-fixed modes, which is validated by normal mode approach. Secondly, the clearance is introduced to one of the spherical joints in the parallel mechanism. The normal and tangential contact forces are calculated based on the Lankarani-Nikravesh contact force model and a modified Coulomb friction model, respectively. In addition, the effect of two coupling relationships on the dynamic response of this parallel mechanism with various thickness of the moving platform is discussed. Finally, the simulation results reveal that the coupling between reference motion and elastic deformation can be ignored in certain situations. However, the coupling between the clearance spherical joint and flexible moving platform deserves more attention, wherein, the flexibility of the moving platform leads to more dramatic collision when its deformation is relatively large, oppositely, it behaves like a dashpot damper to make the system more stable when the deformation is small. This phenomenon also depends on different modal representations.

Learned large field-of-view imaging with thin-plate optics

Typical camera optics consist of a system of individual elements that are designed to compensate for the aberrations of a single lens. Recent computational cameras shift some of this correction task from the optics to post-capture processing, reducing the imaging optics to only a few optical elements. However, these systems only achieve reasonable image quality by limiting the field of view (FOV) to a few degrees - effectively ignoring severe off-axis aberrations with blur sizes of multiple hundred pixels. In this paper, we propose a lens design and learned reconstruction architecture that lift this limitation and provide an order of magnitude increase in field of view using only a single thin-plate lens element. Specifically, we design a lens to produce spatially shift-invariant point spread functions, over the full FOV, that are tailored to the proposed reconstruction architecture. We achieve this with a mixture PSF, consisting of a peak and and a low-pass component, which provides residual contrast instead of a small spot size as in traditional lens designs. To perform the reconstruction, we train a deep network on captured data from a display lab setup, eliminating the need for manual acquisition of training data in the field. We assess the proposed method in simulation and experimentally with a prototype camera system. We compare our system against existing single-element designs, including an aspherical lens and a pinhole, and we compare against a complex multielement lens, validating high-quality large field-of-view (i.e. 53°) imaging performance using only a single thin-plate element.

Impact Dynamics of Single-Layered Graphene Sheets in Multibody Framework Using Nonlocal-Based-ANCF Modeling

A new nonlinear model based on the absolute nodal coordinate formulation (ANCF) and the nonlocal elasticity theory is proposed to investigate the single-layered graphene sheets (SLGSs) impacted by nanoparticles. The geometrical definition of SLGSs is described by using the ANCF thin plate element, and the strain energy is expressed by using the nonlocal theory. The Lennard–Jones pair potential is adopted to model the van der Waals (vdW) force between SLGSs and nanoparticles. The impact dynamics of the system is simulated in multibody framework by using the generalized-alpha numerical integration method. The impact response of the gold atom–SLGSs system is simulated to validate the performance of the proposed model. Three impact dynamic simulations are conducted to investigate the influence of nanoparticles on the impact dynamics of SLGSs. The results show that the coupling of SLGSs vibration and vdW force led to the amplitude inconsistence of [Formula: see text]-position for nanoparticles.

Thin plate element for applied element method

Applied Element Method (AEM) is an efficient method for numerical analysis of structures. It is capable of analyzing the structure up to collapse. In AEM, the structure is modelled as a group of rigid elements connected by springs. It has the benefit of lesser processing time and memory requirement when compared to Finite Element Method. It is also able to track crack propagation more realistically. To extend the advantages of AEM to the analysis of thin plate structures, thin plate element has to be developed. This is done in this paper. Being a rigid body method, AEM does not consider Poisson's ratio in its basic formulation. As Poisson's ratio plays a major role in the behavior of plate structures, the method to bring in Poisson effect in thin plate element is discussed. The procedure to determine displacements, strains, stresses and stress resultants are explained. The mass matrix for thin plate element is also found. To validate the thin plate element, both static and dynamic analyses are carried out. The analyses gave reliable results which show the efficiency of the thin plate element of AEM.

A new locking-free polygonal plate element for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields

A new n-noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The proposed element: (a) has proper rank; (b) passes patch test for both thin and thick plates; (c) is free from shear locking and (d) yields optimal convergence rates in L2-norm and H1-semi-norm. The accuracy and the convergence properties are demonstrated with a few benchmark examples.

Nonlinear Large Deformation of Graphene Sheets Using a Nonlocal-Based ANCF Method

A novel nonlinear model of single-layered graphene sheets (SLGSs) subject to large deformation is proposed using the absolute nodal coordinate formulation (ANCF) and the nonlocal elasticity theory. The geometrical definition of SLGSs is described by ANCF thin plate element while the strain energy is expressed by nonlocal theory. Then, the formulation of elastic force and the Jacobian of the elastic force is derived. We verify the proposed model by comparing the results with other published results and conduct corresponding numerical case study to clarify the influence of boundary conditions (BCs), nonlocal parameters, side length and aspect ratio. Large deformation problem of SLGSs with several BCs and different loading modes are simulated to study the mechanical nonlinearity of the SLGSs.