Elastic Mechanics Problems Research Articles

Isogeometric boundary element method for isotropic damage elastic mechanical problems

In this work, a complex isotropic damage mechanics structural model is developed using the isogeometric method to study the strain displacement and influence factors in isotropically damaged elastics. The proposed modeling method can be constructed dynamically by introducing control points and weight coefficients, which improves the accuracy and eliminates mesh errors, and the boundary element method is used for theoretical analysis and calculation of damage mechanics. For the description of irregular geometric models, the isogeometric method has unparalleled superiority. The isogeometric method can seamlessly connect the geometry generated by the advantages of CAD and CAE, and the combination of the two methods is very useful for the future extension of IGABEM to practical engineering applications. At the same time, we use the source point isolation method to establish the boundary-domain integral equations and use the radial integration method to solve the domain integrals. Compared with the traditional boundary element method, the isogeometric boundary element method makes the construction of complex models simple. The numerical results show that the numerical method has good stability and robustness, which provides strong support for further software integration.

A phase-field method for elastic mechanics with large deformation

Boundary tracking is a challenging numerical problem for elastic mechanics problems with large deformation. In particular, when the boundary conditions rely on the boundary shape, iteration is required between tracking boundaries and solving the elasticity equations. Stability of this iteration brings additional difficulty for designing efficient numerical methods. In this work, we introduce phase-field variables to represent different elastic domains and track the movement of boundaries. Furthermore, boundary conditions relying on the boundary shape can also be easily applied with the phase-field variables. Second-order compact finite difference schemes are used to solve the coupled system on a square-mesh staggered grid. Our numerical results show that the phase-field method can be conveniently used to solve complex elastic mechanics problems accurately.

Analytical and Numerical Modelling of Creep Deformation of Viscoelastic Thick-Walled Cylinder with Fractional Maxwell Model.

The deformation of a thick-walled cylinder under pressure is a classic elastic mechanics problem with various engineering applications. In this study, the displacement of a viscoelastic thick-walled cylinder under internal pressure is investigated via analytical as well as numerical modelling. The fractional Maxwell model is initially introduced to describe the creep deformation of high-strength Q460 steel. Subsequently, an analytical solution to the creep deformation of the thick-walled cylinder under both internal and external pressures is deduced with the corresponding principle. The analytical solution is examined with a numerical simulation that incorporates the fractional Maxwell model by a user-defined subroutine. The numerical simulation agrees well with the analytical solution. The limitations of the current study are also discussed.

Exploring three-dimensional edge-based smoothed finite element method based on polyhedral mesh to study elastic mechanics problems

This paper established the three-dimensional edge-based smoothed finite element method(ES-FEM) based on polyhedral mesh, divided the smoothed domain, constructed the shape function and derived the geometric matrix and the stiffness matrix. The MATLAB software was used to prepare the corresponding computing programs, with which the paper studied the stress distribution of a hollow sphere model and a beam model under different numbers of polyhedral elements. The paper compared the calculation results from the conventional finite element methods(FEM) that use tetrahedral elements and hexahedral elements respectively in terms of stress relative error and energy relative error. The comparison results show that the three-dimensional ES-FEM based on polyhedral mesh has better precision and convergence than the conventional FEM and better adaptability to complex geometric structures.

Numerical solution of functionally graded materials based on radial basis reproducing kernel particle method

In this paper, the radial basis function (RBF) is used to construct the approximating function of the reproducing kernel particle method (RKPM), which can eliminate the negative effect of different kernel functions on the calculating accuracy. The radial basis reproducing kernel particle method (RRKPM) is proposed. Furthermore, the RRKPM is applied to solve the elastic mechanical problems of the functionally graded materials (FGM), and the RRKPM for FGM is established. The corresponding formulae of the RRKPM for FGM are derived. Compared with the traditional RKPM, the RRKPM has higher calculating accuracy and stability. Finally, the numerical examples illustrate that the RRKPM is correct and effective to solve the elastic mechanical problems of the FGM.

Numerical Analysis of Functionally Graded Materials Using Reproducing Kernel Particle Method

The reproducing kernel particle method (RKPM) for the elastic mechanical problems of the functionally graded materials (FGM) is proposed in this paper. The corresponding formulae of the RKPM for the FGM are derived. Furthermore, the control parameter of influence domain radius, penalty factor and different node distribution on the calculation accuracy are discussed. The different functional gradient exponents of the FGM are analyzed. The numerical results illustrate that the RKPM is correct and effective to solve the elastic mechanical problems of the FGM.

Modeling of shear failure in fractured reservoirs with a porous matrix

A finite volume-based numerical modeling framework using a hierarchical fracture representation (HFR) has been developed to compute flow-induced shear failure. To accurately capture the mechanics near fracture manifolds, discontinuous basis functions are employed which ensure continuity of the displacement gradient across fractures. With these special basis functions, traction and compressive forces on the fracture segment can be calculated without any additional constraints, which is extremely useful for estimating the irreversible displacement along the fracture (slip) based on a constitutive friction law. The method is further extended to include slip-dependent hydraulic aperture change and grid convergent results are obtained. Further, the change in hydraulic aperture is modeled using an asymptotic representation which respects the experimentally observed behavior of pore volume dilation due to shear slip. The model allows the initial rapid increase in hydraulic aperture due to shear slip and asymptotically approaches a finite value after repeated shearing of a fracture segment. This aperture increase is the only feedback for mechanics into the fluid flow for a linear elastic mechanics problem. The same model is also extended to include poroelastic relations between flow and mechanics solver. The grid convergence result in the case of poroelastic flow-mechanics coupling for flow-induced shear failure is also obtained. This proves the robustness of the numerical and analytical modeling of fracture and friction in the extended finite volume method (XFVM) set-up. Finally, a grid convergent result for seismic moment magnitude for single fracture and fracture network with random initial hydraulic and friction properties is also obtained. The b-value, which represents the slope of seismic moment occurrence frequency decay vs seismic moment magnitude, which is approximately constant in a semi-logarithmic plot, is estimated. The numerical method leads to converged b-values for both single fracture and fracture network simulations, as grid and time resolutions are increased. For the resulting linear system, a sequential approach is used, that is, first, the flow and then the mechanics problems are solved. The new modeling framework is very useful to predict seismicity, permeability, and flow evolution in geological reservoirs. This is demonstrated with numerical simulations of enhancing a geothermal system.

Analysis about equivalent conversion of two dimensions for large cylinder structure

There was practical engineering of large cylinder structure used in China. Elastic mechanics problems of large cylinder structure quay wall were space problems. Sometimes we needed to transform space problem of large cylinder structure into plane problem of it. Circular section of signal large cylinder structure was converted into rectangular one by using the same bending stiffness and section area for breakwater.

Interpolating Smoothed Particle Method for Elastic Axisymmetrical Problem

The interpolating reproducing kernel particle method is a meshless method with discrete points interpolation character. Coupling this method with the minimum potential energy principle of space axisymmetrical problems of elastic mechanics, the interpolating smoothed particle method (ISPM) is formed. The ISPM, which is a meshless method with discrete points interpolation character, can refrain from quadric error of fitting calculation in stress post-processing by obtaining global domain continuous stress fields directly. This method not only has the advantage in directly exerting boundary conditions just like the finite element method, but is also a new numerical method which has greater computational efficiency and precision than it in solving space axisymmetrical problems of elastic mechanics. Numerical examples are given to show the validity of the new meshless method in the paper.

On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method

AbstractIn order to overcome the possible singularity associated with the Point Interpolation Method (PIM), the Radial Point Interpolation Method (RPIM) was proposed by G. R. Liu. Radial basis functions (RBF) was used in RPIM as basis functions for interpolation. All these radial basis functions include shape parameters. The choice of these shape parameters has been and stays a problematic theme in RBF approximation and interpolation theory. The object of this study is to contribute to the analysis of how these shape parameters affect the accuracy of the radial PIM. The RPIM is studied based on the global Galerkin weak form performed using two integration technics: classical Gaussian integration and the strain smoothing integration scheme. The numerical performance of this method is tested on their behavior on curve fitting, and on three elastic mechanical problems with regular or irregular nodes distributions. A range of recommended shape parameters is obtained from the analysis of different error indexes and also the condition number of the matrix system. All resulting RPIM methods perform very well in term of numerical computation. The Smoothed Radial Point Interpolation Method (SRPIM) shows a higher accuracy, especially in a situation of distorted node scheme.

STRESS FUNCTION OF SIMPLY SUPPORTED CONCRETE BEAM WITH A FRACTURE PROCESS ZONE UNDER UNIFORM LOAD

Based on the weight integration to obtain the closed solution of cohesive crack problem, a method is proposed to obtain the stress function of a simply supported beam under uniform distributed forces in this paper. The key technique is to determine the weight of several solutions of elastic mechanics problems to satisfy the given crack traction within the cohesive crack surfaces and the boundary conditions. The error degree of the function to satisfy the boundary conditions mainly depends on the number and the location of the selected points. In the formed fracture process zone, there is both the finite magnitude of stress concentration and the smooth closed-crack opening displacement. The FE numerical simulation is also carried out; its results are in good agreement with the present theoretical calculation results.

Hypersingularities in three‐dimensional crack configurations in composite laminates

AbstractThree‐dimensional crack configurations in composite laminates are studied by means of the Scaled Boundary Finite Element Method (SBFEM) particularly regarding stress singularities and their associated deformation modes. The SBFEM is an efficient semi‐analytical method that permits solving linear elastic mechanical problems. Only the boundary needs to be discretized while the problem is considered analytically in the direction of the dimensionless radial coordinate pointing from the scaling center to the boundary . An important advantage is that it requires no additional effort for the characterization of existing stress singularities. The situation of two meeting inter‐fiber cracks is investigated in detail, considering different materials and fiber / crack orientations. It is shown that in three‐dimensional crack configurations in composite laminates so‐called hypersingularities can occur, i.e. stress singularities which are even stronger than the classical crack singularity. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Free torsion of thin-walled structural members of open- and closed-sections

Free torsion of thin-walled structures of open- and closed-sections is a classical elastic mechanics problem, which, in literature, is often solved by the method of membrane analogy. The method of membrane analogy, however, can be only applied to structures of a single material. If the structure consists of both open- and closed-sections, the method of membrane analogy is difficult to be applied. In this paper, a new method is presented for solving the free torsion of thin-walled structures of open- and/or closedsections with multiple materials. By utilizing a simple statically indeterminate concept, torsional equations are derived based on the equilibrium and compatibility conditions. The method presented here not only is very simple and easy to understand but also can be applied to thin-walled structures of combined open- and closed-sections with multiple materials.

Stiffness equation of finite segment for flexible beam-formed structural elements

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An explicit tensor expression for the fundamental solutions of a bimaterial space problem

In this paper, by using the method of tensor operation, the fundamental solutions, given in the refernces listed, for a concentrated force in a three-dimensional biphase-infinite solid were expressed in the tensor form, which enables them to be directly applied to the boundary integral equation and the boundary element method for solving elastic mechanics problems of the bimaterial space. The fundamental solutions for Mindlin's problem, Lorentz's problem and homogeneous space problem are involved in the present results.

Elasticity modulus of random composite and elastic percolation failure of solids

The elasticity modulus of random composite is obtained in 2 and 3 dimensional spaces, based on the solutions of over-matching problems in elastic mechanics. A system with 2 components is also considered, and the calculated results are in good agreement with available references. Further, taking the voids and defects in materials as the second phase with zero modulus, one can easily obtain the expressions for predicting modulus and threshold of the elastic percolation failure of materials containing voids, and the results agree excellently with those in available literatures.