Consideration Of Large Deformation Research Articles

Level-set topology optimization considering nonlinear thermoelasticity

At elevated temperature environments, elastic structures experience a change of the stress-free state of the body that can strongly influence the optimal topology of the structure. This work presents level-set based topology optimization of structures undergoing large deformations due to thermal and mechanical loads. The nonlinear analysis model is constructed by multiplicatively decomposing thermal and mechanical effects and introducing an intermediate stress-free state between the undeformed and deformed coordinates. By incorporating the thermoelastic nonlinearity into the level-set topology optimization scheme, wider design spaces can be explored with the consideration of both mechanical and thermal loads. Four numerical examples are presented that demonstrate how temperature changes affect the optimal design of large-deforming structures. In particular, we show how optimization can manipulate the material layout in order to create a counteracting effect between thermal and mechanical loads, even up to a degree that buckling and snap-through are suppressed. Hence the consideration of large deformations in conjunction with thermoelasticity opens many new possibilities for controlling and manipulating the thermo-mechanical response via topology optimization.

Spherical indentation on biological films with surface energy

Micro- and nano-indentations have been widely used to measure the mechanical properties of biological cells and tissues, but the direct application of the classical Hertzian contact model would lead to the overestimation of elastic modulus due to the influence of finite thickness and surface energy. In this work, we analyze spherical indentation of biological films, considering both large deformation and surface energy. The hyperelastic behavior of biological films is characterized by the neo-Hookean model, and the influence of surface energy is addressed through finite element simulation. Based on dimensional analysis, the explicit expressions of load-depth relation accounting for film thickness, large deformation and surface energy are achieved for bonded or non-bonded films. Under a specific load, the consideration of large deformation increases the indent depth, while the finite thickness of films tends to decrease the indent depth, compared to the linear elastic Hertzian solution. More importantly, surface energy evidently alters the load-depth relation for micro-/nano-indentations, which reduces the indent depth and makes the films seemingly stiffer. These results provide a fundamental relationship to accurately extract the mechanical properties of biological films from indentation tests.

Drug Diffusion in a Swollen Polymer

A model of drug diffusion through a polymer matrix that undergoes swelling is presented. The model is based on the Lagrangian description of the swelling dynamics, which allows consideration of large deformations of the polymer matrix. Similarity solutions of a one-dimensional version of the model are determined.

A 2D mechanical–thermal coupled model to simulate material mixing observed in friction stir welding process

The aim of our work is the numerical modeling of two dimensional mechanical–thermal material mixing observed in stir welding process using a high order algorithm. This algorithm is based on coupling a meshless approach, a time discretization, a homotopy transformation, a development in Taylor series and a continuation method. The performance of the proposed model is the consideration of large deformations in the formulation of the posed problem. For the spatial treatment, we use the moving least squares approximation which will be applied directly to the strong form formulation of conservation equations. Each collocation point holds mechanical–thermal variables. The high order algorithm and the homotopy transformation allow reducing the number of tangent matrices to decompose and to avoid iterative procedure. Comparisons with the classical iterative solver (Jamal et al. in J Comput Mech 28:375–380, 2002) are performed. Numerical results reveal that a few number of matrix factorization is needed with the proposed approach, decreasing the computation time.

Size effects on double cantilever beam fracture mechanics specimen based on strain gradient theory

This paper investigates large deformation of a cantilever beam which is further employed to study the fracture behavior of double cantilever beam (DCB), based on strain gradient elasticity theory. Root effect of the DCB is also included for modelling and analyses. The numerical solutions of maximum tip deflection and strain energy release rate are presented. Results demonstrate that the consideration of large deformation is crucial at small scale, especially for more slender beams, as the bending behavior of the beam in that case is different from the classical results. The strain gradient and root effects of the DCB are more prominent when thickness of the beam is less than the material length scale parameter. The strain gradient model demonstrates significant stiffening behavior at the smaller scale. In general, the root effect may not be neglected if the length to thickness ratio of the beam is smaller. Overall, the strain energy release rate of the gradient model, even with the incorporation of root part, remains less than that of non-gradient model. This conclusion is entirely different from the classical method that neglects the uncracked part of the DCB.

Mechanism based nonlinear constitutive model for composite laminates subjected to large deformations

A nonlinear constitutive model for composite laminates is developed with the focus on the distinction among inducing mechanisms. It is shown, that the effect of fiber rotation and damage is essential in consideration of large deformations. The evolution of yielding is described by two independent hardening curves either for in-plane shear or transverse normal load. A method for the experimental determination of the hardening curves is proposed based on uniaxial tests. To ensure the applicability to structural parts, the numerical model is validated by a large number of various angle-ply tension and off-axis compression tests, fabricated of the same carbon/epoxy IM7-8552 material. Extra wide specimen geometry was used for the conducted angle-ply tension tests to prevent delamination failure. The implemented model shows excellent correlation even at very large shear strains of up to 14%.

Study on gob-side entry retaining in fully-mechanized longwall with top-coal caving and its application

Based on the engineering background of gob-side entry retaining in fully-mechanized longwall with top coal caving (GER-FLTC) on N2105 working face of Yuwu coal mine, by adopting the methods of theoretical analysis and numerical calculation, the control techniques of surrounding rocks in GER-FLTC working face are studied in this paper. The two main difficulties of stability of surrounding rocks at gob-side retained entry in fully-mechanized longwall working face are the stability control of top coal and control of large deformation of GER-FLTC working face. Interaction mechanical model between roofing and roadside backfilling in GER-FLTC is established and the equations for the calculation of roof-cutting resistance of roadside backfilling are derived. Results of numerical calculation show that the damage zones of top coal can be categorized into the delaminating zone of top coal above the backfilling, tensile damage zone of top coal above the retained roadway and shear damage zone of the upper rib of the solid coal. Stability control of top coal is the critical part to success of GER-FLTC. With consideration of large deformation of surrounding rocks of gob-side retained entry in fully-mechanized longwall, the support technique of “roofing control and wall strengthening” is proposed where high strength and highly prestressed anchor rods and diagonal tensile anchor cables support are used for top coal, high strength and highly prestressed yielding anchor rod support is used for solid coal and roadside prestressed load-carrying backfilling is constructed by high-water material, in order to maintain the integrity of the top coal, transfer load, high resistance yielding load-carrying of solid coal, roof-cutting of roadside backfilling and support, and to achieve GER-FLTC. Results from this study are successfully applied in engineering practice.

Two-scale computational homogenization of electro-elasticity at finite strains

This contribution addresses a two-scale computational homogenization framework for the simulation of electro-active solids at finite strains. A generalized form of the Hill–Mandel condition is employed for the derivation of energetically consistent transition conditions between the scales. The continuum mechanical formulation is implemented into a two-scale finite element environment, in which we attach a microscopic representative volume element at each integration point of the macroscopic domain. In order to allow for an efficient solution of the macroscopic boundary value problem an algorithmically consistent tangent of the macroscopic problem is derived. The method will be applied to the analysis of dielectric polymer–ceramic composites, where we determine the effective actuation of composites with different microstructures. Furthermore, we show the applicability of the proposed method to the computation of two-scale electro-mechanically coupled boundary value problems in consideration of large deformations.

Damage Assessment of Threaded Connections based on an Advanced Material Model and Local Concepts

In the actual guidelines, for example the German VDI guideline 2230 [1] or the EUROCODE 3 [2], the fatigue assessment of bolted connections and bolts is based on the nominal stress approach. The FKM guideline for analytical strength assessment [3] does not include concepts for a threaded connection, it refers to the existing guidelines as [1]. At present there does not exist any guideline, which provides a damage assessment for general threaded connection by applying local concepts. In the present paper the basics of such a concept are outlined. The investigated metal is 34CrNiMo6, which is generally used for screw threads. The experimental determination of the local stress-strain behaviour in mechanically threaded connections is practically not feasible and needs a numerical approach. This numerical attempt consists of two main tasks, namely the description of the material properties and finite element (FE) analysis. The first one is concerned with the identification of material parameters, which are necessary for the FE analysis, especially for the advanced material model. The experimental work is given by determining the initial monotonic stress- strain curve, the initial unloading curve, the cyclic stress relaxation and cyclic creep. The parameter identification is accomplished using the software MATLAB, which includes the essential nonlinear optimization algorithms. The obtained parameters are entered in the FE software, which is used for the further FE analysis. The distinctive features of the FE analysis are the nonlinearity, especially nonlinear material behaviour, nonlinear contact algorithms and the consideration of large deformations, the high number of load steps and the various load ratio values (R = 0.06 and R = 0.71). The results of the FE analysis are used for the assessment of threaded connections. The damage assessment is realized with the local strain approach based on the damage parameters PSWT and PJ. Finally the result of the simplified method according to Schneider is applied on a high preloaded bolt connection (R = 0.71) and compared with the result achieved with the advanced material model.

Nonlinear Dynamics of Rotors due to Large Deformations and Shear Effects

An analysis of linear and nonlinear dynamics of rotors is presented taking into account the shear effects. The nonlinearity arises due to the consideration of large deformations in bending. The rotor system studied is composed of a rigid disk and a circular shaft. In order to study the combined effect of rotary inertia and shear effects the shaft is modeled as a Timoshenko beam of circular cross section. A mathematical model is developed consisting of 4th order coupled nonlinear differential equations of motion. Method of multiple scales is used to solve these nonlinear equations. Linear and nonlinear dynamic behavior is studied numerically for different values of slenderness ratio r. Resonant curves are plotted for the nonlinear analysis. Due to nonlinearity these curves are of hard spring type. This spring hardening effect is more visible for lower values of r. Also the nonlinear response amplitude is higher when shear deformations are taken into account.

401 流体・構造連成振動を考慮した円筒形貯水タンクの動的座屈解析

This study proposes a dynamic elasto-plastic analysis method which can accurately simulate buckling behavior of cylindrical water storage tanks during earthquake. This proposed method takes into account the behavior of oval-type vibration as well as beam-type vibration. In the proposed method, water in the tanks is modeled and coupled analysis between fluid and structure is adopted in addition to consideration of large deformation of the tank walls. The analytical results by the proposed method have been in good agreement with those of experiment in the matter of occurrence of oval-type vibration, mode of buckling and buckling load.

Collapse analysis of building structures under excitation of near‐fault ground motion with consideration of large deformation and displacement

AbstractThe dynamic analysis of structural stability with consideration of material and geometrical non‐linearity is necessary for near fault‐earthquake that is rich in long‐period components and often induces the non‐linear large displacement and deformation response of a building structure. A macro‐element bilinear geometric stiffness model and simplified analytical model are proposed and developed to analyze the P‐Δ effects of structural dynamic response using a numerical approach. A structural stable threshold diagram is then proposed to evaluate the geometric stability of a building structure with large deformation under the excitation of a near‐fault earthquake. The analysis results reveal: (1) the simplified geometric stiffness analytical model is useful for analyzing structural dynamic P‐Δ effects and acquire very good accurate results even though the structural geometric stiffness varies between elastic and plastic zone; (2) stable threshold diagrams, based on dynamic analysis and statistical analysis procedures, are conducted by application of this proposed model to easily evaluate structural geometric stability with larger deformation imposed by a near‐fault earthquake. This method can supplement the insufficient capability for the static pushover analysis procedure to estimate the seismic proof demands for building without dynamic P‐Δ effects analysis; (3) the analysis results of stable threshold diagrams indicate that when stability coefficient θ of a building is greater than 1 or base shear factor (V/W) of the building is less than 0·2, static P‐Δ effects become noticeable. Copyright © 2007 John Wiley & Sons, Ltd.

Opinion Paper Unexpected Stress Failures during Earthquakes

At present it is the consensus that structures should be desitned to undergo ductile deformations if subjected to very strong ground shaking, so structures designed without consideration of large deformations can be expected to experience undesirable damage. However, in most strong earthquakes some unexpected ground motion or unexpected structural failure occurs which deserves closer examination. In both the Northridge and the Kobe earthquakes there were unexpected ground motions as well as unexpected structural damage. The reason such failures are unexpected is that their possibility was not identified during the design process.