Effects of ball-to-powder diameter ratio and powder particle shape on EDEM simulation in a planetary ball mill

The effects of the ball-to-powder diameter ratio (BPDR) and the shape of the powder particles on EDEM simulation results and time in the planetary ball mill was investigated. BPDR was varied from 1 to 40/3 by changing the powder particle diameter from 8 to 0.6 ?mm. The size and shape of the powder particles do not give a significant change in both the ball motion pattern and simulation results when BPDR is over 20/3. It can be assumed that the kinetic energy of the ball has nothing to do with the size and shape of the powder particle. The simulation time and data size increase exponentially as BPDR increases. The effect of change of the powder particle shape on the calculated data size is not significant, but the more complicated its shape, the longer the simulation time, which is linearly related to the number of spheres composing a particle.     

Isogeometric cable elements based on B-spline curves

Meccanica - In this paper, the isogeometric cable elements based on B-spline curves are developed for the static analysis of cable structures under conservative static loads. For this, the...     

Stability for Leipholz's Type of Laminated Box Columns with Nonsymmetric Lay-Ups on Elastic Foundation

The stability behavior of the Leipholz's type of laminated box columns with nonsymmetric lay-ups resting on elastic foundation is investigated using the finite element method. Based on the kinematic assumptions consistent with the Vlasov beam theory, a formal engineering approach of the mechanics of the laminated box columns with symmetric and nonsymmetric lay-ups is presented. The extended Hamilton's principle is employed to obtain the elastic stiffness and mass matrices, the Rayleigh damping and elastic foundation matrices, the geometric stiffness matrix due to distributed axial force, and the load correction stiffness matrix accounting for the uniformly distributed nonconservative forces. The evaluation procedures for the critical values of divergence and flutter loads with/without internal and external damping effects are briefly presented. Numerical examples are carried out to validate the present theory with respect to the previously published results. Especially, the influences of the fiber angle change and damping on the divergence and flutter loads of the laminated box columns are parametrically investigated.     

Damage Identification of Truss Structures Based on Force Method

An computationally efficient damage identification technique for the planar and space truss structures is presented based on the force method and the micro genetic algorithm. For this purpose, the general equilibrium equations and the kinematic relations in which the reaction forces and the displacements at nodes are take into account, respectively, are formulated. The compatibility equations in terms of forces are explicitly presented using the singular value decomposition (SVD) technique. Then governing equations with unknown reaction forces and initial elongations are derived. Next, the micro genetic algorithm (MGA) is used to properly identify the site and extent of multiple damage cases in truss structures. In order to verify the accuracy and the superiority of the proposed damage detection technique, the numerical solutions are presented for the planar and space truss models. The numerical results indicate that the combination of the force method and the MGA can provide a reliable tool to accurately and efficiently identify the multiple damages of the truss structures.     

Stiffness matrices of thin-walled composite beam with mono-symmetric I- and channel-sections on two-parameter elastic foundation

For the coupled analysis of thin-walled composite beam under the initial axial force and on two-parameter elastic foundation with mono-symmetric I- and channel-sections, the stiffness matrices are derived. The stiffness matrices developed by this study are based on the homogeneous forms of simultaneous ordinary differential equations using the eigen-problem. For this, from the elastic strain energy, the potential energy due to the initial axial force and the strain energy considering the foundation effects, the equilibrium equations and force–displacement relationships are derived. The exact displacement functions for displacement parameters are evaluated by determining the eigenmodes corresponding to multiple non-zero and zero eigenvalues. Then the element stiffness matrix is determined using the force–displacement relationships. For the purpose of comparison, the finite element model based on the classical Hermitian interpolation polynomial is presented. In order to verify the accuracy and the superiority of the beam elements developed herein, the numerical solutions are presented and compared with results from the Hermitian beam elements and the ABAQUS’s shell elements. Particularly, the influence of the initial compressive and tensile forces, the fiber orientation, and the boundary conditions on the coupled behavior of composite beam with mono-symmetric I- and channel-sections is parametrically investigated.     

Dynamic stiffness matrix of thin-walled composite I-beam with symmetric and arbitrary laminations

For the spatially coupled free vibration analysis of thin-walled composite I-beam with symmetric and arbitrary laminations, the exact dynamic stiffness matrix based on the solution of the simultaneous ordinary differential equations is presented. For this, a general theory for the vibration analysis of composite beam with arbitrary lamination including the restrained warping torsion is developed by introducing Vlasov's assumption. Next, the equations of motion and force–displacement relationships are derived from the energy principle and the first order of transformed simultaneous differential equations are constructed by using the displacement state vector consisting of 14 displacement parameters. Then explicit expressions for displacement parameters are derived and the exact dynamic stiffness matrix is determined using force–displacement relationships. In addition, the finite-element (FE) procedure based on Hermitian interpolation polynomials is developed. To verify the validity and the accuracy of this study, the numerical solutions are presented and compared with analytical solutions, the results from available references and the FE analysis using the thin-walled Hermitian beam elements. Particular emphasis is given in showing the phenomenon of vibrational mode change, the effects of increase of the modulus and the bending–twisting coupling stiffness for beams with various boundary conditions.     

Improved torsional analysis of laminated box beams

The improved torsional analysis of the laminated box beams with single- and double-celled sections subjected to a torsional moment is performed by introducing 14 displacement parameters. For this, a thin-walled laminated box beam theory considering the effects of shear and elastic couplings is presented. The governing equations and the force-displacement relations are derived from the variation of the strain energy. The system of linear algebraic equations with non-symmetric matrix is constructed by introducing the displacement parameters and by transforming the higher order simultaneous differential equations into first order ones. This numerical technique determines eigenmodes corresponding to 12 zero and 2 non-zero eigenvalues and derives displacement functions for displacement parameters based on the undetermined parameter method. Finally, the element stiffness matrix is determined using the member force-displacement relations. The theory developed by this study is validated by comparing several torsional responses from the present approach with those from the finite element beam model using the Lagrangian interpolation polynomials and three-dimensional analysis results using the shell elements of ABAQUS for coupled laminated beams with single- and double-celled sections.     

Shear deformable finite beam elements for composite box beams

The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study,numerical solutions are presented and compared with the results obtained by other researchers and the detailed threedimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress–strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated.