Force Equilibrium Conditions Research Articles

Finite Element Analysis of Biot’s Consolidation with a Coupled Nonlinear Flow Model

A nonlinear flow relationship, which assumes that the fluid flow in the soil skeleton obeys the Hansbo non-Darcian flow and that the coefficient of permeability changes with void ratio, was incorporated into Biot’s general consolidation theory for a consolidation simulation of normally consolidated soft ground with or without vertical drains. The governing equations with the coupled nonlinear flow model were presented first for the force equilibrium condition and then for the continuity condition. Based on the weighted residual method, the finite element (FE) formulations were then derived, and an existing FE program was modified accordingly to take the nonlinear flow model into consideration. Comparative analyses using established theoretical solutions and numerical solutions were completed, and the results were satisfactory. On this basis, we investigated the effect of the coupled nonlinear flow on consolidation development.

Free vibration of curved thin-walled rectangular beams

A finite element is presented for the spatial free vibration analysis of horizontally curved thin-walled rectangular box beams. Generalised displacements and generalised coordinates are constructed in accordance with the nine identified cross-section deformation modes, and are employed to formulate the mid-surface contour displacement field. Considering the force-equilibrium condition and the displacement-continuity condition, two different three-dimensional displacement fields of an arbitrary point on the beam are built and used to calculate the strain energy and the kinetic energy of the beam, respectively. With the application of Hamilton's principle, the dynamic equations of the beam are derived; the beam is then approximated with a C0 continuous interpolation function for the finite-element implementation. The validity of this study is confirmed both by the published literature and by Ansys shell theory.

Determination of passive earth pressure coefficients using limit equilibrium approach coupled with the Kötter equation

A numerical method is developed to evaluate the passive earth pressure coefficients for an inclined rigid retaining wall resting against a horizontal cohesionless backfill. A composite failure surface comprises a log spiral, and its tangent is assumed in the present study. The unique failure surface is identified based on the limit equilibrium approach coupled with the Kötter equation (published in 1903). Force equilibrium conditions are used to evaluate the magnitude of the passive thrust, whereas the moment equilibrium condition is employed to determine the location of the passive thrust. The distinctive feature of the present study is that no assumption is required to be made regarding the point of application of the passive thrust, which would otherwise be an essential criterion with respect to the several limit equilibrium based investigations available in the literature. The passive earth pressure coefficients, Kpγ, are evaluated for various values of soil frictional angle [Formula: see text], wall frictional angle δ, and wall inclination angle λ, and compared with the existing results.

A three-dimensional rigorous method for stability analysis and its application

Most traditional methods of three-dimensional (3D) limit equilibrium analysis of slopes have difficulties in satisfying all the equilibrium conditions and in encountering numerical problems in their applications. In this study, the traditional 3D column method is replaced by a new method, providing a better approach to obtain the 3D safety factor. By constructing the normal stresses over the slip surface and considering the equilibrium conditions of the whole sliding body, a 3D slope stability analysis method is proposed, which simultaneously satisfies all six equilibrium conditions and accommodates slip surfaces of any shape. Inter-column force functions are assumed and the distribution function of the normal stress over the slip surface, containing five undetermined parameters, is obtained based on force equilibrium conditions of a typical discretized column. All six equilibrium equations are established considering the whole sliding body in equilibrium, and then the 3D factor of safety is derived using an analytic method. A rigorous and explicit solution is realized and the numerical problems in the 3D analysis procedures of the columns, such as non-convergence and failure of the solution, are thoroughly overcome. Some examples are given to verify the present method. The results demonstrate that the present method is more reliable compared with several other 3D slope stability analysis methods. Finally, this method is successfully applied in stability analysis of the Jinpingzi instability slope. The present 3D slope stability analysis method is easy to implement in computer models and can be widely used by geotechnical engineers for slope design and treatment of landsides.

Theoretical model of static semi-ellipsoidal droplet on a horizontal surface

The objective of this work is to establish a theoretical static force equilibrium equation of the semi-ellipsoidal droplet on a horizontal wall by analyzing the forces acting on the differential element and deducing the expressions of surface tension as well as the internal pressure acting on the droplet. The relationship between the static spreading radius, the density, the volume, the surface tension coefficient and the contact angle of the droplet is given. The results from the equation are compared with the experimental data and show a good agreement. The data from the numerical simulation using the volume of fluid method also agree well with those from the theoretical equation.

Modeling and simulation of partially delaminated composite beams

A finite-element model for beams with partially delaminated layers is used to investigate their behavior. In this formulation account is taken of lateral strains and the first-order shear deformation theory is used. Both displacement continuity and force equilibrium conditions are imposed between the regions with and without delamination. Numerical results of the present model are presented and its performance is evaluated for static and dynamic problems.

Limit equilibrium slope stability analysis using the nonlinear strength failure criterion

The limit equilibrium stability analysis of two- and three-dimensional slopes with the nonlinear failure strength criterion uses a number of variables to determine the normal and shear stress on the slip surface. The equation for the nonlinear strength failure criterion is expressed using a Taylor series after analyzing the stress of an elemental slice or column. Multivariate linear equations are then derived to determine these variables based on the force and moment equilibrium conditions the sliding body is subject to. The stress on the slip surface can also be obtained to calculate the slope safety factor. The validity of the current method was verified by comparing it with established examples. Charts were produced for slope stability analysis with the nonlinear strength failure criterion under general conditions using the current method. The results of this study show that the slope safety factor decreases with an increase in the geotechnical material parameter m in the nonlinear strength failure criterion. The results of the current method are in close correspondence with other traditional limit equilibrium methods and are more reliable than the Swedish method. The charts can be used to determine slope design parameters that meet specific requirements.

Vertical Uplift Capacity of Two Nearby Horizontal Strip Anchors Using the Method of Stress Characteristics

The present study addresses the effect of interference on the uplift capacity of two closely spaced horizontal strip anchors embedded in cohesionless soil. The analysis has been performed using the method of stress characteristics coupled with the limit equilibrium approach. The method consumes fewer assumptions and provides a zone in which the force equilibrium and plastic yield conditions are simultaneously satisfied for given boundary stresses. The effects of surcharge and unit weight of soil on the pullout resistance of anchors have been determined in terms of uplift capacity factors (Fq and Fγ) and are presented as functions of embedment ratio (λ) and angle of internal friction of soil (ϕ). Similarly, the interaction phenomenon of two closely placed anchors has been expressed in terms of efficiency factors (ξq and ξγ). A detailed parametric study has been carried out by varying the clear spacing (S) between two anchors, embedment ratio, and soil friction angle. The results of the numerical analysis are compared with the available theoretical and experimental data reported in the literature.

Analytic Solutions of Shear Lag on Steel-Concrete Composite T‐girder under Simple Bending

The composite T-girders include concrete flange plates and steel beams, which are connected by shear connectors. The longitudinal stress about concrete plate is due to non-uniform distribution on cross section because of the shear lag effect. A differential equation of longitudinal forces at transverse section flange and cantilever flange is separately established according to the strain compatibility and the force equilibrium conditions about a composite T-girder. The method of separation of variables is used to solve the differential equation about the simply supported composite T-girder. The shear lag coefficient is detrmined by the ratio between stress calculated by this method and stress odetrmined by elementary beam theory. An example of such calculation is given to approve its applicability.

Experimental Study on the Axial Force of Shearer Drum Cutting Coal and Rock

The experimental study was carried out on axial force of shearer drum cutting coal and rock on the coal-cutting test bed, in order to find the influence on the axial force of drum structural parameters when shearer drum cutting coal and rock. The structure parameter of drum is the main object of this research. The results of research indicate that when the cone angle of conical pick is equal to 90°, the axial force on both sides has small fluctuation, the coal seam side has small impact on load peak, caused by coal-rock cutting. The cutting line space of conical pick has great influence on axial force of drum. When the cutting line space is about 2.5~3 times as much as cone diameter, the conical pick has equilibrium condition of forces. When the helix angle is equal to 20°, the picks have equilibrium condition of forces, caused by the smaller axial force through the coal charging and coal-rock cutting progress. Seen from the standard deviation of axial force on both sides, sequence drum has more stability and reliability. With the increase of speed, the mean value of the axial force also tends to a steady value, and the axial force on the coal seam side has small fluctuation, which is conducive to the stability and reliability of the shearer during the cutting process. Keywords: Axial force, coal and rock cutting, motion parameters, shearer drum, structural parameters.

Plastic hinge length of reinforced concrete slender shear walls

This paper proposes a simple model that can reasonably determine the potential plastic hinge region for seismic design of shear walls. To idealise the plastic hinge region, a parametric study is conducted on the curvature distribution over the member length using a non-linear, two-dimensional, finite-element analysis procedure. To solve the plastic hinge length equation derived from the idealised curvature distribution, the equations for yielding and ultimate moment capacities of shear walls are generalised on the basis of Bernoulli's principle, strain compatibility condition and equilibrium condition of forces. The generalised equations promise that the yielding and ultimate moment capacities of shear walls can be straightforwardly evaluated with relatively high accuracy. Ultimately, the plastic hinge length of the shear wall is then simply formulated as a function of longitudinal tensile reinforcement index in the boundary element, vertical shear reinforcement index in the web, and axial force index. The predicted plastic hinge lengths obtained from the current simple model are in better agreement with test results than the previous equations; the mean, standard deviation and coefficient of variation of the ratios between experiments and predictions are 1·019, 0·102 and 0·100, respectively.

中部任意位置定向支承加固的压杆稳定性计算

为了丰富压杆的稳定性研究内容和方便工程应用之目的，用初参数法，对中部任意位置增加一个定向支承加固的七种压杆，建立了统一的变形方程和静力平衡方程。由各自的变形和静力约束条件，导出了求解临界压力的特征方程。借助软件，求得了压杆的长度因数与中部支承位置间的近似或精确关系；同时确定了中部支承的最佳位置和最小长度因数，以及最差位置和最大长度因数。经验证，结果符合理论预期。 For enriching the research content about the stability of a long column and making it convenient in the engineering application, by using the initial parameters method, seven kinds of long column are strengthened by directional support in any position of central, and the unified deformation equa-tions and static force equilibrium equations are established. By the respective constraint conditions of deformation and static force, the characteristic equations of critical force are solved. By software, the approximate or accurate relationship between the factor of length of long column and the posi-tion of the central directional support are determined; at the same time, the best position of the central directional support and the minimum factor of length, and the worst position and the maximum factor of length are all determined. The result is verified according with theoretical expectation.

휨 항복형 철근콘크리트 전단벽의 경계요소설계를 위한 변위연성비 모델제시

ABSTRACT This study established a displacement ductility ratio model for ductile design for the boundary element of shear walls. To determine the curvature distribution along the member length and displacement at the free end of the member, the distributio ns of strains and internal forces along the shear wall section depth were idealized based on the Bernoulli’s principle, strain compatibility condition, and equilibrium condition of forces. The confinement effect at the boundary element, provided by transverse reinforcement, was calculated using the stress-strain relationship of confined concrete proposed by Razvi and Saatcioglu. The curvatures corre sponding to the initial yielding moment and 80% of the ultimate state after the peak strength were then conversed into displacement values based on the concept of equivalent hinge length. The derived displacement ductility ratio model was simplified by the regression approach using the comprehensive analytical data obtained from the parametric study. The proposed model is in good agreement with test results, indicating that the mean and standard deviation of the ratios between predictions and experiments are 1.05 a nd 0.19, respectively. Overall, the proposed model is expected to be available for determining the transverse reinforcement ratio at the boundary element for a targeted displacement ductility ratio.

Effect of ionic strength and permeate flux on membrane fouling: Analysis of forces acting on particle deposit and cake formation

In Cross-Flow Microfiltration (CFMF), suspended particles deposit to form a cake layer on the membrane surface, which provides a resistance to permeate flow. The cake resistance, which plays an important role on the performance of CFMF, is mainly determined by the packing porosity of the cake and, the physical and chemical properties of particles. This study aimed at understanding the porosity and the specific filtration resistance of the cake for a given condition. These properties have been studied using experiments under a constant permeate flux. Factors such as permeate flux and ionic strength were investigated in terms of the particles deposition and cake formation. This study also adopted a force balance model to predict the deposit rate of particles and then compare with the experimental results. Inter-particle forces (electric double layer repulsion force and Van der Waals attraction force) were incorporated into the calculation of cake structure (cake porosity and specific resistance) together with the equilibrium condition of hydrodynamic forces. The experimental results showed that the higher the permeate flux led to the greater amount of particles deposit and the denser structure of cake. The porosity of cake decreased with the increase in ionic strength (0∼0.01M) and then increased sharply afterwards (0.01∼0.1M). The hydrodynamic force balance model estimated well the tendency of variation in cake structure depending on the ionic strength.

Solving Internal Forces of Piles of Jointless Bridges under the Action of Temperature Using Ordinary Differential Systems

Temperature effect has a great effect on the force and deformation of bridge abutments, piles and filling at back abutment of jointless bridges. It’s necessary to definitude calculation model when using the finite element method to analyze these matter, but there is still no scientific approach to design jointless bridges. A method that solving internal forces of piles of jointless bridges under the action of temperature using ordinary differential equations is advanced in this paper. Differential equation of each rod of jointless bridges is established based on material mechanic, and then all differential equations form a differential systems. The internal force and deformation of the bridge are getted by solving differential equations based on boundary conditions, deformation coordination of rod coupling points and internal force equilibrium conditions, which is clear and definite.

A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate

This paper investigates the plane problem of a frictional receding contact formed between an elastic functionally graded layer and a homogeneous half space, when they are pressed against each other. The graded layer is assumed to be an isotropic nonhomogeneous medium with an exponentially varying shear modulus and a constant Poisson’s ratio. A segment of the top surface of the graded layer is subject to both normal and tangential traction while rest of the surface is devoid of traction. The entire contact zone thus formed between the layer and the homogeneous medium can transmit both normal and tangential traction. It is assumed that the contact region is under sliding contact conditions with the Coulomb’s law used to relate the tangential traction to the normal component. Employing Fourier integral transforms and applying the necessary boundary conditions, the plane elasticity equations are reduced to a singular integral equation in which the unknowns are the contact pressure and the receding contact lengths. Ensuring mechanical equilibrium is an indispensable requirement warranted by the physics of the problem and therefore the global force and moment equilibrium conditions for the layer are supplemented to solve the problem. The Gauss–Chebyshev quadrature-collocation method is adopted to convert the singular integral equation to a set of overdetermined algebraic equations. This system is solved using a least squares method coupled with a novel iterative procedure to ensure that the force and moment equilibrium conditions are satisfied simultaneously. The main objective of this paper is to study the effect of friction coefficient and nonhomogeneity factor on the contact pressure distribution and the size of the contact region.

An Evaluation of Primer Preseating in Small Caliber Cartridge Production

This work presents the findings of a study to quantify the relative effectiveness of the primer preseating operation in small caliber cartridge production. In theory, primer preseating would enable cartridge stamping tools to achieve deeper stamping penetration depths and subsequently, greater primer retention forces. This is because, with preseating incorporated in the existing small caliber cartridge production process, a cartridge stamping tool would be fully dedicated to performing the case stamping operation (rather than the simultaneous primer seating and case stamping operations it currently performs). The findings presented in this work include measured percentages of total stamping tool force dedicated to primer seating, stamping tool penetration depths with and without primer preseating and primer retention forces with and without primer preseating. These findings and their underlying principles were produced through a static force equilibrium analysis and finite element modeling and simulation studies.

An interactive method of interface boundary elements and partitioned finite elements for local continuous/discontinuous deformation problems

SUMMARYThe interactive method of interface boundary elements (IBEs) and partitioned finite elements (PFEs) is proposed for solving such problems as local continuous/discontinuous deformation (i.e., landslide, concrete cracking, rock mass joints, and internal contraction joints) in concrete dams. The system is divided into continuous displacement bodies and continuous stress joints. The continuous displacement bodies are solved using PFE with the nodal displacements treated as variables, and the rigid displacements in each body and the constraining internal forces on the boundary interface are solved using IBE based on the continuous stress condition and the static force equilibrium condition in each body. Each IBE consists of all interface boundary nodes in a body, and the flexibility matrix is formed using PFE or theoretical analysis. Using this method, a nonlinear iteration procedure is carried out only on the possible discontinuous interface, an approach that greatly improves the computational efficiency. Three numerical examples are used to verify the correctness and validity of the proposed method. © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.

The Study on Differential Equations Method for Solving Column-Pile Structural System Internal Forces

Based on material mechanics theory that loads-internal force-deformation relationship of rod, this paper establish elastic foundation beam model, and establish loads-internal force-deformation differential equation of piles and columns, and identified boundary conditions according to mechanical analysis of piles and columns, Based on the boundary conditions, deformation coordination and internal force equilibrium conditions, solving differential equations, then obtain column - pile components’ internal forces. This method has good mechanical model support, and using mathematical computing software can derive the analytical expressions.

Dynamic Modeling Based on Zero Side-Slip Angle of the Gravity Center for Multi-Axis Steering Vehicles

This paper discovers the dynamic modeling process based on equilibrium condition of forces and moments, in order to improve handling stability, the side-slip angle need to be reduced to zero, special process is used in the dynamic equations simplification for demanded theoretical steering angle of each axel. At last this systems steady-resonance characteristics are researched.