MULTIPLE RECIPROCITY METHOD WITH TWO SERIES OF SEQUENCES OF HIGH-ORDER FUNDAMENTAL SOLUTION FOR THIN PLATE BENDING

The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.

DUAL RECIPROCITY HYBRID BOUNDARY NODE METHOD FOR THREE-DIMENSIONAL ELASTICITY WITH BODY FORCE

Combining Dual Reciprocity Method （DRM） with Hybrid Boundary Node Method （HBNM）, the Dual Reciprocity Hybrid Boundary Node Method （DRHBNM） is developed for three-dimensional linear elasticity problems with body force. This method can be used to solve the elasticity problems with body force without domain integral, which is inevitable by HBNM. To demonstrate the versatility and the fast convergence of this method, some numerical examples of 3-D elasticity problems with body forces are examined. The computational results show that the present method is effective and can be widely applied in solving practical engineering problems.

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method(LKM)with the dual reciprocity method(DRM).Firstly,the temporal derivative is discretized by a finite difference scheme,and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation.Secondly,the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution.And then,the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation,respectively.The LKM is a recently proposed local radial basis function collocationmethod with themerits of being simple,accurate,and free ofmesh and integration.Compared with the traditional domain-type and boundary-type schemes,the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains.Numerical experiments,including two-and three-dimensional heat transfer models,demonstrated the effectiveness and accuracy of the new methodology.

Application of dual reciprocity boundary element method to predict acoustic attenuation characteristics of marine engine exhaust silencers

In marine engine exhaust silencing systems, the presence of exhaust gas flow influences the sound propagation inside the systems and the acoustic attenuation performance of silencers. In order to investigate the effects of three-dimensional gas flow and acoustic damping on the acoustic attenuation characteristics of marine engine exhaust silencers, a dual reciprocity boundary element method (DRBEM) was developed. The acoustic governing equation in three-dimensional potential flow was derived first, and then the DRBEM numerical procedure is given. Compared to the conventional boundary element method (CBEM), the DRBEM considers the second order terms of flow Mach number in the acoustic governing equation, so it is suitable for the cases with higher Mach number subsonic flow. For complex exhaust silencers, it is difficult to apply the single-domain boundary element method, so a substructure approach based on the dual reciprocity boundary element method is presented. The experiments for measuring transmission loss of silencers are conducted, and the experimental setup and measurements are explained. The transmission loss of a single expansion chamber silencer with extended inlet and outlet were predicted by DRBEM and compared with the measurements. The good agreements between predictions and measurements are observed, which demonstrated that the derived acoustic governing equation and the DRBEM numerical procedure in the present study are correct.

APPLICATION OF THE DUAL RECIPROCITY BOUNDARY ELEMENT METHOD TO SOLUTION OF NONLINEAR DIFFERENTIAL EQUATION

In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation del(2) u + u + epsilon u(3) = b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method (DRM) in solving nonlinear differential equations.

Integration of GIS with the Generalized Reciprocal Method(GRM)for Determining Foundation Bearing Capacity:A Case Study in Opolo,Yenagoa Bayelsa State,Nigeria

This study addresses the pressing need to assess foundation bearing capacity in Opolo,Yenagoa,Bayelsa State,Nigeria.The significance lies in the dearth of comprehensive geotechnical data for construction planning in the region.Past research is limited and this study contributes valuable insights by integrating Geographic Information System(GIS)with the Generalized Reciprocal Method(GRM).To collect data,near-surface seismic refraction surveys were conducted along three designated lines,utilizing ABEM Terraloc Mark 6 equipment,Easy Refract,and ArcGIS 10.4.1 software.This methodology allowed for the determination of key geotechnical parameters essential for soil characterization at potential foundation sites.The results revealed three distinct geoseismic layers.The uppermost layer,within a depth of 0.89 to 1.50 meters,exhibited inadequate compressional and shear wave velocities and low values for oedometric modulus,shear modulus,N-value,ultimate bearing capacity,and allowable bearing capacity.This indicates the presence of unsuitable,soft,and weak alluvial deposits for substantial structural loads.In contrast,the second layer(1.52 to 3.84 m depth)displayed favorable geotechnical parameters,making it suitable for various construction loads.The third layer(15.00 to 26.05 m depth)exhibited varying characteristics.The GIS analysis highlighted the unsuitability of the uppermost layer for construction,while the second and third layers were found to be fairly competent and suitable for shallow footing and foundation design.In summary,this study highlights the importance of geotechnical surveys in Opolo’s construction planning.It offers vital information for informed choices,addresses issues in the initial layer,and suggests secure,sustainable construction options.

Singular Hybrid Boundary Node Method for Solving Poisson Equation

As a boundary-type meshless method, the singular hybrid boundary node method（SHBNM） is based on the modified variational principle and the moving least square（MLS） approximation, so it has the advantages of both boundary element method（BEM） and meshless method. In this paper, the dual reciprocity method（DRM） is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution. The general solution is achieved by means of SHBNM, and the particular solution is approximated by using the radial basis function（RBF）. Only randomly distributed nodes on the bounding surface of the domain are required and it doesn＇t need extra equations to compute internal parameters in the domain. The postprocess is very simple. Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable.

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅰ)—RECTANGULAR PLATES WITH FOUR CLAMPED EDGES AND WITH THREE CLAMPED EDGES

In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts: (I) rectangular plates with four damped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates.We arc going to publish them one after another.

RECIPROCAL THEOREM METHOD FOR THE FORCED VIBRATIONOF ELASTIC THICK RECTANGULAR PLATES

In this paper, reciprocal theorem method (RTM) is generalized to solve the problems for the forced vibration of thick rectangular plates based on the Reissner's theory. The paper derives the dynamic basic solution of thick rectangular; and the exact analytical solution of the steady-state responses of thick rectangular plates with three clamped edges and one free edge under harmonic uniformly distributed disturbing forces is found by RTM. It is regarded as a simple, convenient and general method for calculating the steady-stare responses of forced vibration of thick rectangular plates.

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅱ)——RECTANGULAR PLATES WITH TWO ADJACENT CLAMPED EDGES

In this paper, applying the method of reciprocal theorem, we give the distributions of the amplitude of bending moments along clamped edges and the amplitude of deflections along free edges of rectangular plates with two adjacent clamped edges under harmonic distributed and concentrated loads.

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅲ)--CANTILEVER RECTANGULAR PLATES

In this paper,applying the method of the reciprocal theorem,we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic load acting at any point of the plates,the figures and tables of number value of bending moment and the deflection amplitudes as well.

APPLICATION OF THE METHOD OF THE RECIPROCAL THEOREM TO FINDING DISPLACEMENT SOLUTIONS OF CUBES

In this paper the method of reciprocal theorem is extended to find solutions of three-D problems of elasticity.First we give the basic solution of the cube with six surfaces fixed as the basic system and then using the reciprocal theorem between the basic system acted on by unit concentrated loads and the actual system with prescribed surface displacements, we find displacement solution of the actual system.

ON THE METHOD OF RECIPROCAL THEOREM TO FIND SOLUTIONS OF THE PLANE PROBLEMS OF ELASTICITY

In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist, obtaining displacement expressions by means of the method of reciprocal theorem is actual. But in other conditions, when static force edge conditions or mixed ones exist, the obtained displacements are admissible. In order to find actual displacement, the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple, convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions. Evidently, it is a new method.

RECIPROCAL THEOREM METHOD FOR SOLVING THE PROBLEMS OFBENDING OF THICK RECTANGULAR PLATES

In this paper,reciprocal theorem method(RTM) is generalized to solve theof bending of thick rectangular plates based on Reissner’s theory.First,the paper gives the basic solution of the bending of thick rectangular platesand then the exact analytical solution of the bending of thick rectangular plate withthree clamped edges and one free edge under umiformly distributed load is found byRTM, finally, we analyze numerical results of the sohution.

MESHLESS METHOD OF DUAL RECIPROCITY HYBRID RADIAL BOUNDARY NODE METHOD FOR ELASTICITY

Combining the radial point interpolation method （RPIM）, the dual reciprocity method （DRM） and the hybrid boundary node method （HBNM）, a dual reciprocity hybrid radial boundary node method （DHRBNM） is proposed for linear elasticity. Compared to DHBNM, RPIM is exploited to replace the moving least square （MLS） in DHRBNM, and it gets rid of the deficiency of MLS approximation, in which shape functions lack the delta function property, the boundary condition can not be applied easily and directly and it＇s computational expense is high. Besides, different approximate functions are discussed in DRM to get the interpolation property, in which the accuracy and efficiency for different basis functions are compared. Then RPIM is also applied in DRM to replace the conical function interpolation, which can greatly improve the accuracy of the present method. To demonstrate the effectiveness of the present method, DHBNM is applied for comparison, and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM.

Kinematic and Dynamic Characteristics Analysis of Bennett's Linkage

Bennett's linkage is a spatial fourlink linkage,and has an extensive application prospect in the deployable linkages.Its kinematic and dynamic characteristics analysis has a great significance in its synthesis and application. According to the geometrical conditions of Bennett 's linkage,the motion equations are established,and the expressions of angular displacement,angular velocity and angular acceleration of the followers and the displacement,velocity and acceleration of mass center of link are shown. Based on Lagrange's equation,the multi-rigid-body dynamic model of Bennett's linkage is established. In order to solve the reaction forces and moments of joint,screw theory and reciprocal screw method are combined to establish the computing method.The number of equations and unknown reaction forces and moments of joint are equal through adding link deformation equations. The influence of the included angle of adjacent axes on Bennett 's linkage 's kinematic characteristics,the dynamic characteristics and the reaction forces and moments of joint are analyzed.Results show that the included angle of adjacent axes has a great effect on velocity,acceleration,the reaction forces and moments of Bennett's linkage. The change of reaction forces and moments of joint are apparent near the singularity configuration.

Two Dimensional Nanoscale Reciprocating Sliding Contacts of Textured Surfaces

Detailed behaviors of nanoscale textured surfaces during the reciprocating sliding contacts are still unknown although they are widely used in mechanical components to improve tribological characteristics. The current research of sliding contacts of textured surfaces mainly focuses on the experimental studies, while the cost is too high. Molecular dynamics（MD） simulation is widely used in the studies of nanoscale single-pass sliding contacts, but the CPU cost of MD simulation is also too high to simulate the reciprocating sliding contacts. In this paper, employing multiscale method which couples molecular dynamics simulation and finite element method, two dimensional nanoscale reciprocating sliding contacts of textured surfaces are investigated. Four textured surfaces with different texture shapes are designed, and a rigid cylindrical tip is used to slide on these textured surfaces. For different textured surfaces, average potential energies and average friction forces of the corresponding sliding processes are analyzed. The analyzing results show that ＂running-in＂ stages are different for each texture, and steady friction processes are discovered for textured surfaces II, III and IV. Texture shape and sliding direction play important roles in reciprocating sliding contacts, which influence average friction forces greatly. This research can help to design textured surfaces to improve tribological behaviors in nanoscale reciprocating sliding contacts.

THE BENDING OF THIN RECTANGULAR PLATES WITH MIXED SUPPORTED SEGMENTS OF STRAIGHT EDGES

In this paper, the exact analytical solution of the rectangular plate having simplysupported segments mixed with free segments of straight edges are first given by means of the method of reciprocal theorem.By comparison .we calculate the same question by finite element method.Thecomparison shows that the analytical solution is correct.

A Truly Boundary-Only Meshfree Method Applied to Kirchhoff Plate Bending Problems

The boundary particle method(BPM)is a truly boundary-only collocation scheme,whose basis function is the high-order nonsingular general solution or singular fundamental solution,based on the recursive composite multiple reciprocity method(RC-MRM).The RC-MRM employs the high-order composite differential operator to solve a much wider variety of inhomogeneous problems with boundary-only collocation nodes while significantly reducing computational cost via a recursive algorithm.In this study,we simulate the Kirchhoff plate bending problems by the BPM based on the RC-MRM.Numerical results show that this approach produces accurate solutions of plates subjected to various loadings with boundary-only discretization.

Granulation-based LSTM-RF combination model for hourly seasurface temperature prediction

Accurate predictions of sea surface temperature(SST)are crucial due to the significant impact of SST on the global ocean-atmospheric system and its potential to trigger extreme weather events.Many existing machine-learning-based ssT predictions adapt the traditional iterative point-wise prediction mechanism,whose predicting horizons and accuracy are limited owing to the high sensitivity to cumulative errors during iterative predictions.Therefore,this paper proposes a novel granulation-based long short-term memory(LsTM)-random forest(RF)combination model that can fully capture the feature dependencies involved in the fluctuation of SsT sequences,reduce the cumulative error in the iteration process,and extend the prediction horizons,which includes two sub-models(adaptive granulation model and hybrid prediction model).They can restack the one-dimensional ssT time-series into multidimensional feature variables,and achieve a strong forecasting ability.The analysis shows that the proposed model can achieve more accurate prediction-hours in nearly all prediction ranges from 1 to 125 h.The average prediction error of the proposed model in 25-125 h is 0.07 K,similar to that(0.067 K)in the first 24 h,which exhibits a high generalization performance and robustness and isthus a promising platform for the medium-and long-term forecasting of hourly SSTs.