Effect of Refiner Plate Bar Angle and Pulp Properties on the Low Consistency Refining Efficiency in Terms of Power Consumption

Power consumption is the energy source of the impact on fibers or pulp during low-consistency(LC)pulp refining,and the strength of refining affects refining quality and efficiency.The pulp properties,operating parameters,and bar parameters of the refiner plates are important parameters affecting refining efficiency,which can be defined as the ratio of net to total refining power.In this study,LC refining trials for pulps with different consistencies and fiber lengths were conducted using five isometric straightbar plates with different bar angles to explore the influences of the plate bar angle and pulp properties on the no-load power,impact capacity on fibers and refining efficiency.It was found that the no-load power of the LC refining process decreased with an increase in the plate bar angle while increased when pulp with higher consistency was refined under the same refining conditions.However,the effect of pulp consistency on the no-load power can be neglected when refining is conducted using plates with larger bar angles.Meanwhile,a critical bar angle for straight-bar plates in LC refining may exist,which has the strongest impact on the pulp and highest refining efficiency under the same refining conditions.In addition,the impact capacity of the plate on the pulp and refining efficiency in LC refining can be enhanced by appropriately increasing the pulp consistency and average fiber length when the bar angle of the refiner plate with a sector angle of 40°is less than 30°.Therefore,the efficiency and power consumption of the LC refining process can be adjusted by optimizing the pulp consistency and bar parameters of the refining plates.

A refined finite element method for bending analysis of laminated plates integrated with piezoelectric fiber-reinforced composite actuators

This research presents a finite element formulation based on four-variable refined plate theory for bending analysis of cross-ply and angle-ply laminated composite plates integrated with a piezoelectric fiber-reinforced composite actuator under electromechanical loading. The four-variable refined plate theory is a simple and efficient higher-order shear deformation theory, which predicts parabolic variation of transverse shear stresses across the plate thickness and satisfies zero traction conditions on the plate free surfaces. The weak form of governing equations is derived using the principle of minimum potential energy, and a 4-node non-conforming rectangular plate element with 8 degrees of freedom per node is introduced for discretizing the domain. Several benchmark problems are solved by the developed MATLAB code and the obtained results are compared with those from exact and other numerical solutions, showing good agreement.

A two variable refined plate theory for the bending analysis of functionally graded plates

Bending analysis of functionally graded plates using the two variable refined plate theory is presented in this paper.The number of unknown functions involved is reduced to merely four,as against five in other shear deformation theories. The variationally consistent theory presented here has, in many respects,strong similarity to the classical plate theory. It does not require shear correction factors,and gives rise to such transverse shear stress variation that the transverse shear stresses vary parabolically across the thickness and satisfy shear stress free surface conditions.Material properties of the plate are assumed to be graded in the thickness direction with their distributions following a simple power-law in terms of the volume fractions of the constituents.Governing equations are derived from the principle of virtual displacements, and a closed-form solution is found for a simply supported rectangular plate subjected to sinusoidal loading by using the Navier method.Numerical results obtained by the present theory are compared with available solutions,from which it can be concluded that the proposed theory is accurate and simple in analyzing the static bending behavior of functionally graded plates.

Isogeometric analysis for free vibration of bidirectional functionally graded plates in the fluid medium

This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate change in both the thickness and length directions via power-law distributions and Mori-Tanaka model. The governing equation of motion of BDFG plate in the fluid-plate system is formulated basing on Hamilton's principle and the refined quasi three-dimensional (3D) plate theory with improved function f(z). The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to determine the added mass. The discrete system of equations is derived from the Galerkin weak form and numerically analyzed by IGA. The accuracy and reliability of the proposed solutions are verified by comparing the obtained results with those published in the literature. Moreover, the effects of the various parameters such as the interaction boundary condition, geometric parameter, submerged depth of plate, fluid density, fluid level, and the material volume control coefficients on the free vibration behavior of BDFG plate in the fluid medium are investigated in detail. Some major findings regarding the numerical results are withdrawn in conclusions.

Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

Development of quadrilateral spline thin plate elements using the B-net method

The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.

Static Analysis of Functionally Graded Sandwich Plates Using an Efficient and Simple Refined Theory

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Two common types of functionally graded sandwich plates, namely, the sandwich with fimctionally graded facesheet and homogeneous core and the sandwich with homogeneous facesheet and functionally graded core, are considered. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinu- soidal loading has been obtained by using the Navier method. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded sandwich plates.

Forced vibration of smart laminated viscoelastic plates by RPT finite element approach

In this study,a finite element formulation based on the four-variable refined plate theory(RPT)is presented for forced vibration analysis of laminated viscoelastic composite plates integrated with a piezoelectric layer.To the best of the authors’knowledge,this is the first time that the proposed approach is extended for study of the dynamic behavior of the smart viscoelastic plate.The utilized RPT which works for both thick and thin plates predicts a parabolic variation for transverse shear stresses across the plate thickness.Considering a linear viscoelastic model for the substrate material,the relaxation module is predicted by the Prony series.Using Hamilton’s principle,the weak form equation is constructed and a four-node rectangular plate element is utilized for discretizing the domain.The Newmark scheme is employed for advancing the solution in time.A MATLAB code is developed based on the formulations and several benchmark problems are solved.Comparing the findings with existing results in previous studies confirms the accuracy and efficiency of the proposed method.The dynamic response of the smart viscoelastic plates under various electromechanical loads is investigated and the results show that the.vibration can be passively controlled by adding and actuating the piezoelectric layer.The damping effects of viscoelastic parameters on the results are investigated,too.

Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory

This work presents a theoretical study for thermo-mechanical buckling of size-dependent magneto-electro-thermo-elastic func-tionally graded(METE-FG)nanoplates in thermal environments based on a refined trigonometric plate theory.Temperature field has uniform,linear,and nonlinear distributions across the thick-ness.Nonlinear thermal loadings are considered as heat conduc-tion(HC)and sinusoidal temperature rise(STR).A power law function is applied to govern the gradation of material properties through the nanoplate thickness.Considering coupling impacts between magneto,electro,thermo-mechanical loadings,the equa-tions of motion,and distribution of magneto-electrical field across the thickness direction of the METE-FG nanoplate are derived.The exact solutions for critical buckling temperatures of METE-FG nanoplates are introduced implementing Navier’s method.Moreover,the accuracy of the present formulation is examined by comparing the obtained results with published ones.Furthermore,the effects played by the magneto-electrical field,various temperature rises,nonlocality,power law index,side-to-thickness ratio,and aspect ratio on the critical buckling tempera-ture response are all investigated and reported.

Elastic Wave Scattering and Dynamic Stress Concentrations in Stretching Thick Plates with Two Cutouts by Using the Refined Dynamic Theory

Based on the refined dynamic equation of stretching plates, the elastic tensio compression wave scattering and dynamic stress concentrations in the thick plate with two cutouts are studied. In view of the problem that the shear stress is automatically satisfied under the free boundary condition, the generalized stress of the first-order vanishing moment of shear stress is considered. The numerical results indicate that, as the cutout is thick, the maximum value of the dynamic stress factor obtained using the refined dynamic theory is 19% higher than that from the solution of plane stress problems of elastic dynamics.

Multi-layered plate finite element models with node-dependent kinematics for smart structures with piezoelectric components

This article presents a type of plate Finite Element(FE)models with adaptive mathematical refinement capabilities for modeling laminated smart structures with piezoelectric layers or distributed patches.The p-version shape functions are used in combination with the higher-order Layer-Wise(LW)kinematics adopting hierarchical Legendre polynomials.Node-Dependent Kinematics(NDK)is employed to implement local LW models in the regions with piezoelectric components and simulate the global substrate structure with the Equivalent Single-Layer(ESL)approach.Through the proposed NDK FE models,the electro-mechanical behavior of smart structures can be predicted with high fidelity and numerical efficiency,and various patch configurations can be conveniently modeled through one set of mesh grids.Moreover,the effectiveness and efficiency of the NDK FE approach are assessed through numerical examples and its application is demonstrated.