Theorems on the limit analysis of finite deformation

A generalized variational principle (theorem 1) which is equivalent mathematically to the whole set of equations and conditions and must be satisfied by the limit analysis of finite deformation is proposed in this paper. It is also proved that the limit load deduced from theorem 1 will lie between the lower and upper bounds given by the bound theorems of finite deformation     

SLIP-LINE FIELD THEORY OF PLANE PLASTIC STRAIN DEALING WITH MOHR’S CRITERION EXPRESSED BY QUADRATIC LIMITING CURVES

In this paper, the slip-line field theory of plane plastic strain dealing with Mohr’s criterion expressed by quadratic limiting curves is preliminarily established. It takes the classical slip-line field theory as its special case, and it can be applied to the analysis of plane-strain problems in metal processing, rock and soil mechanics and tectonomechanics. As preliminary application, the slip-line field and limiting loads of flat punch indenting problem are determined by numerical solution, and the slip-line field of bedded medium gravity-sliding problem is determined and discussed.     

Effect of yield stress on the flow of a Casson fluid in a homogeneous porous medium bounded by a circular tube

The effect of yield stress on the flow characteristics of a Casson fluid in a homogeneous porous medium bounded by a circular tube is investigated by employing the Brinkman model to account for the Darcy resistance offered by the porous medium. The non-linear coupled implicit system of differential equations governing the flow is first transformed into suitable integral equations and are solved numerically. Analytical solution is obtained for a Newtonian fluid in the case of constant permeability, and the numerical solution is verified with that of the analytic solution. The effect of yield stress of the fluid and permeability of the porous medium on shear stress and velocity distributions, plug flow radius and flow rate are examined. The minimum pressure gradient required to start the flow is found to be independent of the permeability of the porous medium and is equal to the yield stress of the fluid.     

Upper bound limit analysis of active earth pressure with different fracture surface and nonlinear yield criterion

Conventional calculations of static and seismic active earth pressures of soils on a retaining wall are formulated assuming the soils obeying a linear Mohr–Coulomb yield criterion. However, experimental evidences show that the strength envelopes of almost all geomaterials are nonlinear in nature over a wide range of normal stresses. In this paper, the strength envelope of the backfill behind a retaining wall is considered to follow a nonlinear yield criterion. A simple method is proposed for calculating the static and seismic active earth pressures acting against a retaining wall using a nonlinear yield criterion. This method is based on the upper bound theorem of limit analysis. Both translational and rotational fracture surfaces are employed in the formulation for calculating active earth pressures. Quasi-static representation of earthquake effects using a seismic coefficient concept is adopted for seismic active earth pressure calculations. Instead of using directly the actual nonlinear yield criterion, a linear Mohr–Coulomb yield criterion, which is tangential to the nonlinear yield criterion, is used to formulate the active earth pressure problem as a classical nonlinear programming problem. A nonlinear sequential quadratic programming algorithm is used to search for the maximum solution. In order to assess the validity of the proposed method, values of active earth pressures for different values of seismic coefficients and nonlinear parameters in the yield criterion are calculated and compared with solutions obtained using an extended Rankine’s active earth pressure theory. For the case of static active earth pressure, the upper bound solutions using the present method with a translational fracture surface are equal to the extended Rankine’s theoretical solutions and are slightly smaller than those obtained using the present method with a rotational fracture surface. For the case of seismic active earth pressure, numerical results obtained using the present method with a rotational fracture surface is very close to the extended Rankine’s theoretical solutions. A study is conducted to investigate the effects of the parameters in the nonlinear yield criterion on the active earth pressures.     

Invariant analysis of the Reynolds stress tensor for a nuclear fuel assembly with spacer grid and split type vanes

Invariant analysis of the Reynolds stress tensor anisotropy can give an accurate and deep intuitive understanding of the turbulent structure of a turbulent flow. Lumley's triangle has proven to be a powerful representation of the invariant analysis of the second-order statistics collection provided by the Reynolds stress tensor. In the present work the spectral element code Nek5000 has been used to investigate the turbulent structure of the flow across a pressurized water reactor spacer grid with split type mixing vanes. Wall-resolved large eddy simulation of the flow in a prototypical rod bundle geometry at Re = 14,000 and P/D = 1.32 are performed and validated against particle image velocimetry data. The results are then used to perform an in-depth invariant analysis. The results show a reorganization of the Reynolds stresses components in the downstream region of the spacer grid. The mixing vanes orientation produces a symmetric behavior between sub-channels. The turbulent structure in the fully developed region has the typical behavior of fully-developed channel flow turbulence. When averaging the state across regions of the sub-channels, we observed a transition from disk-like turbulence in the mixing vanes region to rod-like turbulence in the fully developed region.     

Study on the generalized prandtl-reuss constitutive equation and the corotational rates of stress tensor

I.IntroductionTilepl'ogl'ess11as.toifcertainextent,beenmadeintheelastic-plasticconstitutivetheoryatII[litedefbrlllations.Coil'paredwitllotherconstitutiverelations,thegeneralizedPrandtlReuss(P-R)equatiollsareextensivelystudiedandwidelyapplied.IndevelopingthegeneralizedP-Requation.itisusuallyassumedthatthedeformationrate(thesymmetricpartorvelocitygradiellt)isdecolllposedintotheelasticpartandplasticpart.TheplasticLIcf\'l.llliltlollrittcobeystilenormalfi(,xvrilleasillthecaseofinfinitcsilllnld…     

A mathematical theory of materials with elastic range and the definition of back stress tensor

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Original Article On the frame dependence and form invariance of the transport equations for the Reynolds stress tensor and the turbulent heat flux vector: its consequences on closure models in turbulence modelling

The present paper shows that the transport equations governing second order turbulent closures are form invariant, but remain frame dependent through the emergence of the body force; thus they do not fulfil the principle of material frame indifference as formulated by Truesdell & Noll (1965). However, this frame dependence corresponds to that first discussed by Müller (1972) and today developed in the framework of the new concept of extended thermodynamics. Following this new concept, these relations are consequently incorporated as additional basic balance laws. The results are: 1) in the case of the Reynolds-stress-transport equation, this eliminates the so-called constraints imposed in [15–17, 19] on turbulence models; 2) to ensure the closure of the new set of basic balance laws, closure assumptions can then be considered as proper constitutive equations which must be restricted by the well known constitutive theory principles in extended thermodynamics. Received: April 4, 1996     

Exact analysis of Burgers equation on semiline with flux condition at the origin

The initial boundary value problem for the Burgers equation in the domain x 0, t > 0 with flux boundary condition at x = 0 has been solved exactly. The behaviour of the solution as t tends to infinity is studied and the “asymptotic profile at infinity” is obtained. In addition, the uniqueness of the solution of the initial boundary value problem is proved and its inviscid limit as → 0 is obtained.     

Modeling the interfacial effect on the yield strength and flow stress of thin metal films on substrates

It is shown in this paper that interfacial effects have a profound impact on the scale-dependent yield strength and strain hardening rates (flow stress) of metallic thin films on elastic substrates. This is achieved by developing a higher-order strain gradient plasticity theory based on the principle of virtual power and the laws of thermodynamics. This theory enforces microscopic boundary conditions at interfaces which relate a microtraction stress to the interfacial energy at the interface. It is shown that the film bulk length scale controls the size effect if a rigid interface is assumed whereas the interfacial length scale dominates if a compliant interface is assumed.     

Elasto-plastic analysis of Reissner-Mindlin plates by the use of hybrid stress FEM with layered model

Based on a _mR -type variational formulation featuring a cross-depth layered model in conjunction with a mechanical sub-element for simulating the material constitution, the cross-depth plasticity development of the Reissner-Mindlin plate is investigated by following the loading process. A 4-node quadrilateral hybrid-stressc ⁰-continuous plate-bending element HPT-9 is formulated. Numerical examinations demonstrate its remarkable characteristic behavior in being free from spurious kinematic mode, capable of alleviating locking difficulties as the thin plate limit is approached and providing numerical results with remarkable accuracy and computational efficiency over Spilker's counterpart LH₄. An elasto-plastic analysis of Reissner-Mindlin plates has justified the validity and effectiveness of the present scheme in depicting the cross-depth plasticity development following the loading process.The Project is Supported by National Natural Science Foundation of China.     

Bifurcation analysis in the system with the existence of two stable limit cycles and a stable steady state

Van der Pol–Duffing oscillator, which can be used a model for many dynamical system, has been widely concerned. However, most of the systems by scholars are either stable steady states or limit cycles. Here, the self-sustained oscillator with the coexistence of steady state and limit cycles, which is famous for describing the flutter of airfoils with large span ratio in low-speed wind tunnels, is treated in this paper. Using the energy balance method, the deterministic bifurcation of the tristable system with time-delay feedback is investigated. The presence of time-delay feedback expands the bifurcation range of the parameters, making the bifurcation phenomenon more abundant. In addition, according to the stationary probability density function obtained by the stochastic averaging method, stochastic bifurcation of the system with time-delay feedback and noise is explored theoretically. The numerical results confirm the correctness of the theoretical analysis. Transition between the unimodal structure, the bimodal structure and the trimodal structure is found. Many rich bifurcations are available by adjusting the time-delay and noise intensity, which may be conductive to achieve the desired phenomenon in the real-world application.

     

Efficient computation of order and mode of three-dimensional stress singularities in linear elasticity by the boundary finite element method

The Boundary Finite Element Method (BFEM), a novel semi-analytical boundary element procedure solely relying on standard finite element formulations, is employed for the investigation of the orders and modes of three-dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates. After a comprehensive literature review and a concise introduction to the standard three-dimensional BFEM formulation for the static analysis of general unbounded structures, we demonstrate the application of the BFEM for the computation of the orders and modes of two-dimensional and three-dimensional stress singularities for several classes of problems within the framework of linear elasticity. Special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates. In all cases, the BFEM computations agree excellently with available reference results. The required computational effort is found to be considerably lower compared to e.g. standard Finite Element Method (FEM) computations. In the case of free laminate corners, numerous new results on the occurring stress singularities are presented. It is found that free-corner problems generally seem to involve a more pronounced criticality than the corresponding free-edge situations.     

Limit analysis by linear programming of 3D masonry structures with associative friction laws and torsion interaction effects

In this paper, a formulation for limit analysis of three-dimensional masonry structures discretized as rigid block assemblages interacting through no-tension and frictional contact interfaces is developed. Linear and piecewise linearized yield functions are used for rocking, sliding and torsion failure. A simple yield condition has been defined to take into account interaction effects of shear force with torsion and bending moment. Associative flow rules are considered for strain rates. On the basis of the developed governing equations, the limit analysis problem has been formulated as a nonlinear mathematical program. An iterative solution procedure based on linear programming is used to solve the limit analysis problem and to take into account nonlinearities due to the influence of bending moments and shear stresses on torsion strength. The results of experimental investigations on out-of-plane masonry walls constrained at one edge and different examples from literature were considered for validation. Comparison with existing formulations is carried out.