Kinematics and Dynamics of Deployable Structures with Scissor-Like-Elements Based on Screw Theory

Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element（SLE）. First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. Screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.

Bending of small-scale Timoshenko beams based on the integral/differential nonlocal-micropolar elasticity theory: a finite element approach

A novel size-dependent model is developed herein to study the bending behavior of beam-type micro/nano-structures considering combined effects of nonlocality and micro-rotational degrees of freedom. To accomplish this aim, the micropolar theory is combined with the nonlocal elasticity. To consider the nonlocality, both integral (original) and differential formulations of Eringen’s nonlocal theory are considered. The beams are considered to be Timoshenko-type, and the governing equations are derived in the variational form through Hamilton’s principle. The relations are written in an appropriate matrix-vector representation that can be readily utilized in numerical approaches. A finite element (FE) approach is also proposed for the solution procedure. Parametric studies are conducted to show the simultaneous nonlocal and micropolar effects on the bending response of small-scale beams under different boundary conditions.

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.

Conversion between solid and beam element solutions of finite element method based on meta-modeling theory:development and application to a ramp tunnel structure

In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.

Calculation of the Coupling Coefficient of Twin-Core Fiber Based on the Supermode Theory with Finite Element Method

Currently, coupled mode theory (CMT) is widely used for calculating the coupling coefficient of twin-core fibers (TCFs) that are used in a broad range of important applications. This approach is highly accurate for scenarios with weak coupling between the cores but shows significant errors in the strong coupling scenarios, necessitating the use of a more accurate method for coupling coefficient calculations. Therefore, in this work, we calculate the coupling coefficients of TCFs using the supermode theory with finite element method (FEM) that has higher accuracy than CMT, particularly for the strong coupling TCF. To investigate the origin of the differences between the results obtained by these two methods, the modal field distributions of the supermodes of TCF are simulated and analyzed in detail.

Perturbation Theory Combined with Boundary Element Method for Analysis of Gear Contact Problems

This paper combines the perturbation theory with the boundary element methodfor contact problems of three-dimensional elasticity mechanism to analyse the effect oferrors on the shape of the contact area and pressure distribution in gear drive through theperturbation of a cubic order geometry,there by greatly bringing down both computationwork volume and cost and providing a powerful tool for engineering study on the effectof errors on structural strength.

Quadrilateral 2D linked-interpolation finite elements for micropolar continuum

Quadrilateral finite elements for linear micropolar continuum theory are developed using linked interpolation.In order to satisfy convergence criteria,the newly presented finite elements are modified using the Petrov-Galerkin method in which different interpolation is used for the test and trial functions.The elements are tested through four numerical examples consisting of a set of patch tests,a cantilever beam in pure bending and a stress concentration problem and compared with the analytical solution and quadrilateral micropolar finite elements with standard Lagrangian interpolation.In the higher-order patch test,the performance of the first-order element is significantly improved.However,since the problems analysed are already describable with quadratic polynomials,the enhancement due to linked interpolation for higher-order elements could not be highlighted.All the presented elements also faithfully reproduce the micropolar effects in the stress concentration analysis,but the enhancement here is negligible with respect to standard Lagrangian elements,since the higher-order polynomials in this example are not needed.

Finite element implementation of poroelasticity theory for swelling dynamics of hydrogels

Abstract Hydrogel can swell to many times of its dry volume, resulting in large deformation which is vital for its function. The swelling process is regulated by many physical and chemical mechanisms, and can, to some extent, be fairly described by the poroelasticity theory. Implementation of the poroelastieity theory in the framework of finite element method would aid the design and optimization of hydrogel-based soft devices. Choosing chemical potential and displacement as two field variables, we present the implementation of poroelastieity tailored for hydrogel swelling dynamics, detail the normalization of physical parameters and the treatment of boundary conditions. Several examples are presented to demonstrate the feasibility and correctness of the proposed strategy.

18-DOF Triangular Quasi-Conforming Element for Couple Stress Theory

The basic idea of quasi-conforming method is that the strain-dis-placement equations are weakened as well as the equilibrium equations.In this paper,an 18-DOF triangular element for couple stress theory is proposed within the framework of quasi-conforming technique.The formulation starts from truncated Taylor expansion of strains and appropriate interpolation functions are chosen to calculate strain integration.This element satisfies C0 continuity with second order accuracy and weak C1 continuity simultaneously.Numerical examples demonstrate that the proposed model can pass the C0??1 patch test and has high accuracy.The element does not exhibit extra zero energy modes and can capture the scale effects of microstructure.

Vibration analysis of two-dimensional structures using micropolar elements

Based on the micropolar theory(MPT),a two-dimensional(2 D)element is proposed to describe the free vibration response of structures.In the context of the MPT,a 2 D formulation is developed within the ABAQUS finite element software.The user-defined element(UEL)subroutine is used to implement a micropolar element.The micropolar effects on the vibration behavior of 2 D structures with arbitrary shapes are studied.The effect of micro-inertia becomes dominant,and by considering the micropolar effects,the frequencies decrease.Also,there is a considerable discrepancy between the predicted micropolar and classical frequencies at small scales,and this difference decreases when the side length-to-length scale ratio becomes large.

Simulation of bulk metal forming processes using one-step finite element approach based on deformation theory of plasticity

The bulk metal forming processes were simulated by using a one-step finite element(FE)approach based on deformation theory of plasticity,which enables rapid prediction of final workpiece configurations and stress/strain distributions.This approach was implemented to minimize the approximated plastic potential energy derived from the total plastic work and the equivalent external work in static equilibrium,for incompressibly rigid-plastic materials,by FE calculation based on the extremum work principle.The one-step forward simulations of compression and rolling processes were presented as examples,and the results were compared with those obtained by classical incremental FE simulation to verify the feasibility and validity of the proposed method.

The Influence of Alkaline Earth Elements on Electronic Properties ofα-Si3N4 via DFT Calculation

We used density functional theory(DFT)calculations to study the influence of alkali earth metal element(AE)doping on the crystal structure and electronic band structure ofα-Si3N4.The diversity of atomic radii of alkaline earth metal elements results in structural expansion when they were doped into theα-Si3N4 lattice.Formation energies of the doped structures indicate that dopants prefer to occupy the interstitial site under the nitrogen-deficient environment,while substitute Si under the nitrogen-rich environment,which provides a guide to synthesizingα-Si3N4 with different doping types by controlling nitrogen conditions.For electronic structures,energy levels of the dopants appear in the bottom of the conduction band or the top of the valence band or the forbidden band,which reduces the bandgap ofα-Si3N4.

A New Rectangular Finite Element Formulation Based on Higher Order Displacement Theory for Thick and Thin Composite and Sandwich Plates

A new displacement based higher order element has been formulated that is ideally suitable for shear deformable composite and sandwich plates. Suitable functions for displacements and rotations for each node have been selected so that the element shows rapid convergence, an excellent response against transverse shear loading and requires no shear correction factors. It is completely lock-free and behaves extremely well for thin to thick plates. To make the element rapidly convergent and to capture warping effects for composites, higher order displacement terms in the displacement kinematics have been considered for each node. The element has eleven degrees of freedom per node. Shear deformation has also been considered in the formulation by taking into account shear strains ( rxz and ryz) as nodal unknowns. The element is very simple to formulate and could be coded up in research software. A small Fortran code has been developed to implement the element and various examples of isotropic and composite plates have been analyzed to show the effectiveness of the element.

THE RATIONALISM THEORY AND ITS FINITE ELEMENT ANALYSIS METHOD OF SHELL STRUCTURES

In this paper, a kind of rationalism theory of shell is established which is of different mechanic characters in tension and in compression, and the finite element numerical analysis method is also described.

The Dao of Mathematical Creativity,Symmetry Theories,and Yin-Yang Philosophy With Their Classroom Applications

This paper introduces creativity,one of the significant features in maths.The creative mathematical beauty of symmetry and asymmetry are worth investigating in the practicing of Taichi.Symmetrical variances make the real world.Symmetry can be regarded as a kind of mirroring,like the line symmetry,the mirror image of the other parts,or rotational symmetry.Such characteristics can be vividly demonstrated in the traditional Chinese philosophical yin-yang theory(YY).The accompanying of male and female reveals the friendly cooperative relationship.YY reflects the counterparts of vacancy and firm,inhale and exhale,noun and verb,theory and practice,light and heavy,slow and fast,the pace,the sound effect in the classroom.Such an analysis is undergone about yin and yang in Yi School and Dao De Ching(DDC).Furthermore,there are detailed arguments of the symmetric nature of every verse of DDC,revealing the cultural value of the language.Their applications in the class admit the recognition under the new liberal arts project by China’s Ministry of Education.Yet,the integration of research and teaching is required to go further.

The Application of Ecological Elements of Digital Technology in Construction Industry

The application of digital technology in the field of construction is still in its infancy, and the existing concrete framework of digital technology application in the construction industry and the study of applied ecological elements are not enough. The ecological elements of digital technology application in the construction industry are important factors that promote the healthy operation of the entire digital technology application ecosystem. Using grounded theory, we compiled the data of 33 researchers who participated in semi-structured interviews, and obtained 4 main categories and 9 sub-categories of ecological elements of digital technology application in the construction industry. Among them, the digital technology application mechanism is the core category of ecological application elements. We also used the Bass model to analyze the application trend of digital technology in the construction industry. In 2040, the number of construction companies applying digital technology will reach 98.66% of the maximum market potential.

Gender Relations in Kjell Askildsen’s A Lovely Place From the Perspective of Chinese Yin-Yang Theory

A Lovely Place(2019)is a collection of the Norwegian writer Kjell Askildsen’s short stories that is translated from German into Chinese by Yang Zhizi.It contains 18 short stories,whose male characters are mainly analyzed by researchers.The paper argues that female characters are playing an indispensable role in compensating the males’life stories and enlightening their worldviews according to Chinese Yin-Yang theory.The females can be classified into the following three groups in terms of their important relations to the males.Firstly,the female is the male’s companion in a certain part of the latter’s life.Secondly,the female facilitates the male’s intellectual growth either spontaneously or purposefully.Thirdly,the female struggles for independence to set an example for the male.The female characters in A Lovely Place present such femininity as beauty,energy,nostalgia,sentimentality,motherhood,etc.,stimulate the males to reflect on their own identities and fulfill their muscularity,and function as the genuine protagonists in the collection as far as the gender relations are concerned.

STUDY ON THE FRACTAL CHARACTER OF MAGNETIC ANOMALY FIELDS AND THE DELINEATION OF TECTONIC ELEMENTS IN THE SOUTH CHINA SEA

This is a quantitative method for studying the fractal character of magnetic anornaly fields and delineating tectonic elements using fractal theory . For an area with different geological and geophysical features , the definition of Hausdorff dimension is used to calculate the fractal dimension of the area’s magnetic field , then delineate geological tectonic elements by comparing this value . Use of 1978- 1986 geophysical survey data in this method applied to the South China Sea yielded three first grade tectonic elements and nine second grade ones , in six of which subsecond grade elernents were found.

INFLUENCE OF THE FIVE ELEMENT THEORY ON ACUPUNCTUROLOGY

In the present paper, the authors make a simple comment on the influence of the theory of five elements of TCM on the acupuncturology from ① its influence on the meridian-collateral theory and acupoint system; ② its influence on acu-moxibustion therapeutics including the application of mother and son points for reinforcing and reducing, the application of the five element theory to the midnight-noon ebb-flow needling, and guiding point selection in different seasons; and ③ its influence on acupuncture techniques.