Nodal Deformation Research Articles

Vector form intrinsic finite element analysis for nonlinear parametric resonances of planar beam structures

The parametric resonance of a beam structure may lead to a disastrous consequence. To assess the safety of a structure, structural engineers need a straightforward and practical method to calculate the large-amplitude nonlinear parametric resonance responses of the beam structure. This paper proposes a newly developed vector form intrinsic finite element (VFIFE) calculation scheme to analyse the nonlinear parametric resonance of planar beam structures. By taking into account the geometric stiffness effect of the internal axial force for the frame element, a new relationship between internal nodal forces and deformation components is first established based on the VFIFE principle and the parametric resonance mechanism of frame structures. A numerical example of a portal frame is presented to demonstrate the efficacy of this new calculation scheme. A parametric resonance test of the cantilever beam is conducted to verify the applicability of the VFIFE method. The numerical results show that the proposed scheme can well simulate the nonlinear phenomena of parametric resonances. The numerical predictions are consistent with the experimental observations. A filtering-based finite-time Lyapunov exponent approach is presented to determine the stability boundary of the structure. The numerical stability boundary of parametric resonance agrees well with the experimental boundary. Possible causes of deviations between the numerical and experimental results are discussed. The proposed VFIFE scheme is a simple and effective means of analysing the stability and nonlinear responses of the parametric resonance of planar beam structures.

Static analysis of functionally graded porous beam-column frames by the complementary functions method

In this paper, an efficient and accurate numerical approach is implemented to examine the static behavior of Functionally Graded Porous (FGP) planar frames for the first time. The symmetric material constitutive relationship (SMCR), monotonic material constitutive relationships (MMCR), and uniform material constitutive relationship (UMCR) models are used to define the gradation of porosity along the thickness direction. The effects of porosity coefficient and material porosity distribution type on the static behavior of the FGP frames are investigated in detail. A direct relation between porosity coefficient and nodal deformations is observed.The effect of shear deformation is considered in the governing equations based on the Timoshenko Beam Theory (TBT). Within the scope of the presented procedure, fifth-order Runge-Kutta (RK5) algorithm is applied in the solution of the initial value problems. Imposing the rigidity matrix-based Complementary Functions Method (CFM) on the static analysis of the FGP planar frames is the novelty of this research. The results of the suggested approach are verified with the those of the finite element method (FEM), and those of the available literature. It has been carried out that type of the porosity distribution and porosity gradient index have an important impact on the response of FGP planar frames. By increasing the porosity coefficient, the displacement values of the frames made of UMCR and MMCR porosity distribution are affected more than those of the UMCR distributions. It can be noted that the SMCR can be preferred for designing the FGP beam-column structure as the minimum deformation values are obtained.

The Vibration Attenuation Characteristics of Dynamic Vibration Absorbers Array for Tuned and Mistuned Bladed Disk

Abstract Dynamic vibration absorbers array (DVAA) is a newly developed and promising technique for vibration attenuation of integrally bladed disk (blisk) by mounting underneath the disk. In this paper, the vibration attenuation characteristics and energy dissipation mechanism of DVAA for tuned and mistuned blisk are parametrically studied, where the viscous and frictional damping are both considered. The lumped parameter model of a blisk is employed for the convenience of parametrical study. Analytical power flow formulas within the blisk–DVAA system are derived to characterize the dynamic interaction between blisk and DVAA. Four typical modes of a blisk with different nodal diameters and deformation characteristics are selected to evaluate the performance of DVAA. Then, the effects of the mass ratio, the frequency ratio and the damping ratio of DVAA on the vibration of tuned and mistuned blisk are addressed. Numerical results show that a light DVAA can significantly mitigate the resonant amplitudes of the tuned and mistuned blisk. Such damper is effective for the modes with different modal characteristics and can provide robust vibration attenuation performance against random mistuning.

A multinode superelement in the generalized strain formulation

Design and optimization of flexure mechanisms and real time high bandwidth control of flexure based mechanisms require efficient but accurate models. The flexures can be modeled using sophisticated beam elements that are implemented in the generalized strain formulation. However, complex shaped frame parts of the flexure mechanisms could not be modeled in this formulation. The generalized strain formulation for flexible multibody analysis defines the configuration of elements using a combination of absolute nodal coordinates and deformation modes.This paper defines a multinode superelement in this formulation, i.e., an element having its properties derived from a reduced linear finite element model. This is accomplished by defining a local element frame with the coordinates depending on the absolute nodal coordinates. The linear elastic deformation is defined with respect to this frame, where rotational displacements are defined using the off-diagonal terms of local rotation matrices. The element frame can be defined in multiple ways; the most accurate results are obtained if the resulting elastic rotations are as small as possible. The inertia is defined in two different ways: the so-called “full approach” gives more accurate results than the so-called “corotational approach” but requires a special term that is not available from standard finite element models. Simulations show that (flexure based) mechanisms can be modeled accurately using smart combinations of superelements and beam elements.

The Interference Effects of Wind Load and Wind-Induced Dynamic Response of Quayside Container Cranes

Strong wind has caused damage to group-arranged quayside container cranes in terminals and ports in recent years. Interference may amplify the wind loads in some cases. However, the interference effect among cranes has rarely been studied. In this study, high-frequency force balance tests were conducted to obtain the wind load of isolated and group-arranged container cranes. The results of the computational fluid dynamics simulation were validated by wind tunnel tests and provided the mean wind loads of all 15 types of member cranes. According to the results from wind tunnel tests, the fluctuating wind loads of each member were generated using the weighted amplitude wave superposition method. Based on dynamic finite element methods, the wind-induced responses were obtained considering the interference effect. It was found that the interference effect is the combined effects of both the shielding effect and the amplification of turbulence. Although in some cases the fluctuating and peak wind loads can increase by up to 16% and 6%, respectively, those in the most unfavorable cases are reduced by the interference effect. The interference factor for extreme nodal deformation is 0.56 and 0.69. The interference effect in container cranes mainly appears as a shielding effect, reducing the wind loads and response of the structures in unfavorable cases.

Nodal-line semimetal HMTSF-TCNQ: Anomalous orbital diamagnetism and charge density wave

This study investigates the electronic states and physical quantities of an organic charge-transfer complex HMTSF-TCNQ, which undergoes a charge-density-wave (CDW) phase transition at temperature $T_c\simeq 30$ K. A first-principles calculation is utilized to determine that the normal state is a topological semimetal with open nodal lines. Besed on the first-principles calculation, we develop a tight-binding model to investigate the electronic state in detail. Below $T_c$, the CDW phase is examined in the tight-binding scheme using the mean-field approximation. It is shown that the open nodal lines are deformed into closed ones, and their shapes are sensitive to the order parameter. Using this tight-binding model, we theoretically evaluate the temperature dependencies of two physical quantities: the spin-lattice relaxation time $T_1$ and the orbital magnetic susceptibility. In particular, an anomalous plateau is obtained at low temperatures in the orbital diamagnetism. We presume that this anomalous plateau originates owing to the conflict between the interband diamagnetism, impurity scattering, and the nodal line deformation. We also conduct an experiment to investigate the orbital magnetism, and the results are in excellent quantitative agreement with the theory.

Multi-Objective Teaching-Learning-Based Optimization for Structure Optimization

ABSTRACT Teaching–learning-based optimization is a specific parameter-free and powerful algorithm. However, in large and diverse spaces it often gets trapped in local optima and faces criticism of premature convergence particularly while solving multi-objective problems. The present work proposed a novel multi-objective teaching–learning-based optimization (MOTLBO) based on the framework of non-dominated sorting and solution storage in an external archive. These techniques improve the algorithm’s speed of search and convergence rate. Moreover, this mechanism also assists in obtaining a Pareto optimal set near to the true Pareto solutions while simultaneously maintaining the diversity among non-dominated solutions within one run. The present work proposed a novel MOTLBO. To determine feasibility for practical applications, perceived structure design problems are exposed to multiple and diverse weight minimization and maximization of nodal deformation objectives. The suggested algorithm is employed to five challenging optimization issues of the structure having discrete design variables and subject to multiple constraints. For a performance check, the suggested algorithm is contrasted with two prominent multi-objective algorithms. The performance gauge for all considered test examples is the Pareto front hypervolume and front spacing-to-extent test. MOTLBO shows its promise with coherence and diversification of solutions for producing the desired Pareto fronts.

Multiscale Modelling and Mechanical Anisotropy of Periodic Cellular Solids with Rigid-Jointed Truss-Like Microscopic Architecture

This paper investigates the macroscopic anisotropic behavior of periodic cellular solids with rigid-jointed microscopic truss-like architecture. A theoretical matrix-based procedure is presented to calculate the homogenized stiffness and strength properties of the material which is validated experimentally. The procedure consists of four main steps, namely, (i) using classical structural analysis to determine the stiffness properties of a lattice unit cell, (ii) employing the Bloch’s theorem to generate the irreducible representation of the infinite lattice, (iii) resorting to the Cauchy–Born Hypothesis to express the microscopic nodal forces and deformations in terms of a homogeneous macroscopic strain field applied to the lattice, and (iv) employing the Hill–Mandel homogenization principle to obtain the macro-stiffness properties of the lattice topologies. The presented model is used to investigate the anisotropic mechanical behavior of 13 2D periodic cellular solids. The results are documented in three set of charts that show (i) the change of the Young and Shear moduli of the material with respect to their relative density; (ii) the contribution of the bending stiffness of microscopic cell elements to the homogenized macroscopic stiffness of the material; and (iii) polar diagrams of the change of the elastic moduli of the cellular solid in response to direction of macroscopic loading. The three set of charts can be used for design purposes in assemblies involving the honeycomb structures as it may help in selecting the best lattice topology for a given functional stiffness and strength requirement. The theoretical model was experimentally validated by means of tensile tests performed in additively manufactured Lattice Material (LM) specimens, achieving good agreement between the results. It was observed that the model of rigid-joined LM (RJLM) predicts the homogenized mechanical properties of the LM with higher accuracy compared to those predicted by pin-jointed models.

Multi-criteria decision making for lower bumper stiffener material change in a sports utility vehicle with CAE simulation

This article describes the steps to replace the lower bumper stiffener material of a sport utility vehicle. It was taken as the main characteristics to obtain the behaviour principles as the lower bumper stiffener. A static structural simulation was developed according to the regulation of physical trials of the EuroNCAP. Three multi-criteria selection methods called TOPSIS, VIKOR and ENTROPY were applied. Polylactic acid was determined as the optimal material. A dynamic simulation between of the contact of the leg form impactor and pedestrian protection system, at a speed of 40 km/h was performed. The simulation evaluates the acceleration of the tibia, equivalent strain of Von Misses and deformation in the three nodes of the lower bumper stiffener. It was determined that the optimal material is the PLA, where it is appreciated that the main factors to consider for the decision making is the acceleration and the nodal deformation of the dynamic simulation.

Singular Welschinger invariants

We suggest an invariant way to enumerate nodal and nodal-cuspidal real deformations of real plane curve singularities. The key idea is to assign Welschinger signs to the counted deformations. Our invariants can be viewed as a local version of Welschinger invariants enumerating real plane rational curves.

Multi-criteria selection methods (MCDM) for lower bumper stiffener material change in a Sports Utility Vehicle with CAE simulation

This article describes the steps to replace the lower bumper stiffener material of a sport utility vehicle. It was taken as the main characteristics to obtain the behaviour principles as the lower bumper stiffener. A static structural simulation was developed according to the regulation of physical trials of the EuroNCAP. Three multi-criteria selection methods called TOPSIS, VIKOR and ENTROPY were applied. Polylactic acid was determined as the optimal material. A dynamic simulation between of the contact of the leg form impactor and pedestrian protection system, at a speed of 40 km/h was performed. The simulation evaluates the acceleration of the tibia, equivalent strain of Von Misses and deformation in the three nodes of the lower bumper stiffener. It was determined that the optimal material is the PLA, where it is appreciated that the main factors to consider for the decision making is the acceleration and the nodal deformation of the dynamic simulation.

Deformation of singular fibers of genus two fibrations and small exotic symplectic 4-manifolds

We introduce the [Formula: see text]-nodal spherical deformation of certain singular fibers of genus two fibrations, and use such deformations to construct various examples of simply connected minimal symplectic [Formula: see text]-manifolds with small topology. More specifically, we construct new exotic minimal symplectic [Formula: see text]-manifolds homeomorphic but not diffeomorphic to [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text] using combinations of such deformations, symplectic blowups, and (generalized) rational blowdown surgery. We also discuss generalizing our constructions to higher genus fibrations using [Formula: see text]-nodal spherical deformations of certain singular fibers of genus [Formula: see text] fibrations.

A resolution of singularities for Drinfeld’s compactification by stable maps

Drinfeld’s relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of singularities consisting of stable maps from nodal deformations of the curve into twisted flag varieties. As an application, we prove that the twisted intersection cohomology sheaf on Drinfeld’s compactification is universally locally acyclic over the moduli stack of G G -bundles at points sufficiently antidominant relative to their defect.

Comparison of Deformation Models of Flexible Manipulator Joints for Use in DEMO

The joint deformation contributes significantly to final end-effector displacement of a manipulator, especially when the manipulator is in the form a serial kinematics with long links. When the manipulators employed in the DEMO are under the heavy payload, the deformation of manipulator is inevitable and the magnitude is significant. In order to maneuver the large object through several via points with high positioning accuracy in the remote handling process of DEMO, the real-time computation of manipulator deformation has to be conducted, which is crucial to the DEMO adaptive position control system for the displacement compensation. Three computation-effective deformation modeling methods are proposed in this paper, which are parametric modeling method, nonparametric deterministic artificial neural network (ANN) modeling method, and nonparametric Bayesian ANN modeling method, respectively. A specific joint in a boom equipped in a telescopic articulated remote mast is taken as the study object in this paper. A nodal deformation in the joint is investigated by three modeling methods, respectively. The parametric deformation model is derived by using the structural mechanics, whose parameters are identified by using the Markov chain Monte Carlo (MCMC) method; the deformation model of deterministic ANN is trained by using the Levenberg–Marquardt method; and the deformation model of the Bayesian ANN is trained by using the MCMC method. The results show that the parametric model from the structural mechanics is linear and is incompetent in the deformation modeling when the nonlinearity presents; both the deterministic and Bayesian ANNs are capable of model the nodal deformation of joint. The performance of both the deterministic network and Bayesian network cannot rival for one another in the application scenario of this paper. The training of the Bayesian network can provide the criterions for estimation of possible ranges of the modeling outputs from its probabilistic distribution curves, and the judgment of proper size of network.

Static contact analysis of spiral bevel gear based on modified VFIFE (vector form intrinsic finite element) method

• A new method to determine the theoretical formulas of the 8-node hexahedral entity element for the VFIFE method was developed. • Matching contact algorithms are proposed and combined with the VFIFE method. • Finite element model of a spiral bevel gear pair was established and analyzed by the VFIFE method. • The computational accuracy of the VFIFE models with different mesh densities was discussed and summarized. Since the intrinsic limitations of FEM (Finite element method) and lumped-mass method, we derive the formula of 8-node hexahedral element based on VFIFE (vector form intrinsic finite element method) method and applied it in contact analysis of gears. This paper proposed a new method to determine pure nodal deformation, which could simplify the computation compared to the traditional VFIFE method. Combining the VFIFE method and matching contact algorithm, we analyzed spiral bevel gear meshing problems. Spiral bevel models with two different mesh densities are calculated analyzed by the VFIFE method and FEM. Performance indicators of gears are extracted and compared, including contact forces, contact and bending stresses, contact stress patterns and loaded transmission errors. The results show that the VFIFE method has a stable performance and reliable accuracy under coarse or refined mesh conditions, while the FEM inaccurately calculates the contact stress of the coarse mesh model. The examples demonstrate that the proposed method could precisely analyze gear meshing problems with a coarse mesh model, which provides a new solution for gear mechanics.

Solid structure analysis with large deformation of eight-node hexahedral element using vector form intrinsic finite element

The vector form intrinsic finite element method has been proposed to deal with large deformation and complex non-linear problems in structural analysis. However, the study of method is mainly limited in plane element. This article expands the application range of the vector form intrinsic finite element method by deriving the formula of eight-node hexahedral element. A new method to determine pure nodal deformation was proposed and described in detail, which could simplify the computation comparing to the traditional vector form intrinsic finite element method. Compared with the finite element method and other methods in three different numerical examples, the numerical results of this method show a good reliability and accuracy in large deformation problems. This method lays the foundation for solving three-dimensional solid problems by vector form intrinsic finite element method in structural engineering fields.

Evaluation of nanoindentation load-depth curve of MEMS bridge structures by calculating the critical elastic-plastic bending deflections

This paper proposes a correction method to accurately evaluate the nanoindentation load-depth (P-h) curve of MEMS double clamped micro bridge structures. Critical elastic and plastic deflections of the bent bridge are extracted from the overall elastic-plastic deflection, respectively. Through subtracting the elastic-plastic deflection of the micro bridge from the total displacement of the Berkovich indenter’s tip, the effect of constraint condition (double clamped) on the P-h curve of micro bridge is corrected. Nanoindentation P-h curves of routine and micro bridge C11000 Cu specimens are respectively obtained and compared with each other through both finite element analysis and experiments. Meanwhile, cross-sectional profiles along the symmetry axis of local indentation locations respectively obtained from the nodal deformations and scanned images of routine and micro bridge specimens are also compared and explained. Furthermore, a theoretical model is proposed to analyze the effect of the equivalent flow area induced by the elastic-plastic deflection on maximum indentation depth, the corrected values of Young’s modulus, maximum and residual depths of micro bridge specimens are essentially in agreement with that of routine fixed specimens.

A computational model for atomistic-based higher-order continua using the FEM technique

In this paper, an atomistic-based higher-order continuum model is developed in the framework of nonlinear finite element method to present the geometrically nonlinear behavior of nano-structures. In order to model the inhomogeneous deformation within the Cauchy-Born hypothesis, the higher-order CB hypothesis is presented based on a hierarchical multi-scale technique, in which the constitutive model of higher-order continuum is obtained using the derivatives of strain energy density. In order to avoid the use of C1–continuity element, as an alternative procedure, the mixed-type element is utilized employing the nodal deformation gradient as additional degrees of freedom. The relation between the nodal displacement DOFs and the nodal deformation gradient DOFs are enforced using the Lagrange-multipliers method. Finally, the efficiency of the proposed multi-scale technique in capturing the geometrically nonlinear behavior of nano-structures is illustrated through several numerical examples. The influence of higher-order terms in the Cauchy-Born hypothesis is presented by comparing the numerical results with those obtained from the classical CB hypothesis. A study on mesh size dependence of the proposed multi-scale technique is performed for numerical simulations with distinct levels of mesh size.

Modeling the operation of a screw L-shaped knife of a tiller

During the operation, standard L-shaped knives are exposed to various loads. The shape of the L-shaped knife blades does not meet the requirement of performing sliding cutting, which leads to an increase in the energy intensity of milling the soil. To ensure optimal cutting conditions without weed-covering and knife blocking, it is necessary that in any section of the blade (in the plane of rotation) the angle of its setting у (cutting) is constant. Therefore, the blade of the knife should be made on a screw line, which will ensure its smooth entry and sliding cutting when moving in the soil. The purpose of the study is to improve the quality and reduce the energy consumption of soil cultivation by selecting a rational angle for installing the blade and optimizing the parameters of the screwed L-shaped cutter blades. To study the work and the loading process of the screw L-shaped cutter knife, the finite element method was used from the APM FEM application library of the KOMPAS-3D system. The design of the knife was broken into elements to show their movements and deformations through the displacements of the boundary points (knots) of the element, then the nodal displacements, deformations and stresses were determined. In the course of the study, the dependence of the values of linear displacements and stress values was studied depending on the angle of installation of the knife blade (у = 35° ... 60°). The results of the study showed that as the angle of the blade was increased to у = 60 °, the total linear displacements decreased by 18 % reaching 0,6978 mm, compared to у = 35 ° (0,8455 mm) at a maximum load of 2000 N. The knife with an installation angle у = 60° has safety factor values higher than a knife with у = 35° for all load stages (500, 1000, 1500 and 2000 N). The screw knife with a large installation angle is most suitable for milling soil with slip, which is typical for sod processing. As a result of the research it was proposed to use knives with a screw working surface for milling the soil with high quality.

Resistance of Concrete Slender Columns

The paper presents a calculation of slender concrete column resistance with a non-linear analysis which takes into account a contribution of second order theory, non-linear distribution of concrete stresses in cross-section and cracking. The Transfer Matrix Method was used as a step by step method for calculation of nodal forces and deformation vectors and modified rigidities of reinforced concrete segments. Also Newton method for searching equivalence of normal forces and bending moments on each step of calculation and central cross-section of column segment is explained in details. Theoretical results are compared with another non-linear software and realized experiment.