Non-Linear Vibrations of Plates Under Thermal and Mechanical Loads

The geometrically non-linear vibrations of plates under the combined effect of thermal fields and mechanical excitations are analyzed. With this purpose, an accurate model based on a p-version, hierarchical, first-order shear deformation finite element is employed. The constitutive material of the plates is linear elastic and isotropic. The equations of motion are solved in the time domain by an implicit time integration method. The temperature and the amplitude of the mechanical excitation are varied, and transitions from periodic to non-periodic motions are found.

Minimum Rank Generalized Subspace Updating Approach for Nonlinear Systems

An algorithm for analyzing a nonlinear system as an augmented linear system is presented. The method uses a nonlinear discrete model of the system and the form of the nonlinearities to create an augmented linear model of the system. A linear modal analysis technique that uses forcing that is known but not prescribed is then used to solve for the modal properties of the augmented linear system after the onset of damage. Due to the specialized form of the augmentation, nonlinear damage causes asymmetric damage in the updated matrices. A generalized minimum rank perturbation theory, which requires knowledge of both right and left eigenvectors, is developed to handle the asymmetric damage scenarios. The damage extent algorithm becomes an iterative process when an incomplete set of right eigenvectors are known. The method is demonstrated using numerical data from nonlinear 3-bay truss structures. Various damage scenarios of the nonlinear systems are used to demonstrate the effectiveness of the augmentation and the generalized minimum rank perturbation theory, and the effect of random noise on the technique. The nonlinearities included in the 3-bay truss are cubic springs.

A Method to Extract Interface Stress Intensity Factors Using Interlayers

A method is presented here to extract stress intensity factors for interface cracks in plane bimaterial fracture problems. The method relies on considering a companion problem wherein a very thin elastic interlayer is artificially inserted between the two material regions of the original bimaterial problem. The crack in the companion problem is located in the middle of the interlayer with its tip located within the homogeneous interlayer material. When the thickness of the interlayer is small compared with the other length scales of the problem, a universal relation can be established between the actual interface stress intensity factors at the crack tip for the original problem and the mode I and II stress intensity factors associated with the companion problem. The universal relation is determined by formulating and solving a boundary value problem. This universal relation now allows the determination of the stress intensity factors for a generic plane interface crack problem as follows. For a given interface crack problem, the companion problem is formulated and solved using the finite element method. Mode I and II stress intensity factors are obtained using the modified virtual crack closure method. The universal relation is next used to obtain the corresponding interface stress intensity factors for the original interface crack problem. An example problem involving a finite interface crack between two semi-infinite blocks is considered for which analytical solutions exist. It is shown that the method described above provides very acceptable results.

A Micro-Damage Model for High Velocity Impact Using Combined Viscosity and Gradient Localization Limiters

During dynamic loading processes, large inelastic deformation associated with high strain rates leads, for a broad class of ductile metals, to degradation and failure by strain localization. However, as soon as material failure dominates a deformation process, the material increasingly displays strain softening and the finite element computations are considerably affected by the mesh size and alignment. This gives rise to a non-physical description of the localized regions. This paper presents theoretical and computational frameworks to solve this problem with the aid of nonlocal gradient-enhanced theory coupled to visco-inelasticity. Constitutive equations for anisotropic thermo-viscodamage (rate-dependent damage) mechanism coupled with thermo-hypoelasto-viscoplastic deformation are developed in this work within the framework of thermodynamic laws, nonlinear continuum mechanics, and nonlocal continua. Explicit and implicit micro-structural length scale measures, which preserve the well-posedness of the differential equations, are introduced through the use of the viscosity and gradient localization limiters.

A New Approach for Modeling of Fatigue Crack Growth in Welded Cruciform and Curve T Joint Structures

A new approach for the simulation of fatigue crack growth in welded joint has been developed and the concept has been applied to welded cruciform and curve T-joints. The phenomena of crack propagation and interface debonding can be regarded as the formation of new surface. Thus, it is possible to model these problems by introducing the mechanism of surface formation. In the proposed method, the formation of new surface is represented by interface element based on the interface potential energy. The properties of this interface element represent the bonding strength of the material. As the cyclic load continues, the bonding strength decreases between the interacting surfaces and the crack propagates slowly. Based on this concept, an ANSYS code has been written for the simulation of crack propagation. Using this code, fatigue crack growth rate and fatigue crack propagation life of 2-D FEM models of welded cruciform and curve T-joints for different stress/load ratios have been analyzed and presented in this paper. The method is relatively simple compared to other conventional FEM method and save computer time significantly. The predicted results are compared with experimental results and good agreement has been achieved.

Rate-Dependent Cohesive Zone Modeling of Unstable Crack Growth in an Epoxy Adhesive

This paper presents the development and numerical implementation of a rate dependent fracture model of an epoxy adhesive. Previous mode I fracture tests conducted under quasistatic, displacement controlled loading of an aluminum double cantilever beam (DCB) bonded with the epoxy exhibited unstable crack growth in the adhesive. Results from mode I fracture tests of compact tension specimens made from bulk adhesive at increasing cross head opening speeds are reported in this paper. The compact tension tests results showed a decreasing critical strain energy release rate with increasing cross head speed, with the critical energy release rate at 1 m/s cross head speed equal to about 20% of its quasi-static value. Two rate dependent cohesive zone models are formulated based on the compact tension test data. A cohesive de-cohesive relationship was postulated between the tractions acting across the crack faces and the opening displacement and opening velocity. These rate dependent cohesive zone models are implemented in a interface finite element to model discrete crack growth in the adhesive. The reaction force history from simulation of the DCB test is in good agreement with the test data using only the rate dependent interface element to model the adhesive.

Simulation of Fracture Behavior of Elastomer Modified Polypropylene Based on Elastoviscoplastic Constitutive Equation With Craze and Tensile Softening Law

The strong strain-rate dependence, neck propagation and craze evolution characterize the large plastic deformation and fracture behavior of polymer. In the latest study, Kobayashi, Tomii and Shizawa suggested the elastoviscoplastic constitutive equation based on craze evolution and annihilation and then applied it to the plane strain issue of polymer. In the previous study, the author applied their suggested elastoviscoplastic constitutive equation with craze effect to the three dimensional shell issue and then showed that the load displacement history was in good agreement with the experimental result including only microscopic crack such as craze. For the future industrial applications, the macroscopic crack had to be taken into account. For instance, an airbag deployment simulation needed the macroscopic crack prediction. Thus, the main objective of this study was to propose the tensile softening equation and then add it to the elastoviscoplastic constitutive equation with craze effect so that the load displacement history could be roughly simulated during the macroscopic crack propagation. The tested material in this study was the elastomer blended polypropylene used in the interior and exterior of automobiles. First, the material properties were obtained based on the tensile test results at wide range of strain rates: 10−4 – 102 (1/sec). Next, the fast compact tension test was conducted and then the tensile softening parameters were fixed. Then, the fast bending test and the dart impact test were carried out in order to obtain the load displacement history and also observe the macroscopic crack propagation at high strain rate. Finally, the fracture behavior was simulated and then compared with the experimental results. It was shown that the predictions of the constitutive equation with the proposed tensile softening equation were in good agreement with the experimental results.

Nonlinear Vibrations of Rectangular Plates With Different Boundary Conditions: Theory and Experiments

Large-amplitude vibrations of rectangular plates subjected to harmonic excitation are investigated. The von Ka´rma´n nonlinear strain-displacement relationships are used to describe the geometric nonlinearity. A specific boundary condition, with restrained normal displacement at the plate edges and fully free in-plane displacements, not previously considered, has been introduced as a consequence that it is very close to the experimental boundary condition. Results for this boundary condition are compared to nonlinear results previously obtained for: (i) simply supported plates with immovable edges; (ii) simply supported plates with movable edges, and (iii) fully clamped plates. The nonlinear equations of motion are studied by using a code based on arclength continuation method. A thin rectangular stainless-steel plate has been inserted in a metal frame; this constraint is approximated with good accuracy by the newly introduced boundary condition. The plate inserted into the frame has been measured with a 3D laser system in order to reconstruct the actual geometry and identify geometric imperfections (out-of-planarity). The plate has been experimentally tested in laboratory for both the first and second vibration modes for several excitation magnitudes in order to characterize the nonlinearity of the plate with imperfections. Numerical results are able to follow experimental results with good accuracy for both vibration modes and for different excitation levels once the geometric imperfection is introduced in the model. Effects of geometric imperfections on the trend of nonlinearity and on natural frequencies are shown; convergence of the solution with the number of generalized coordinates is numerically verified.

High Strain Rate Tensile Behavior of Carbon Fiber Reinforced Aluminum Laminates

In this paper, loading and loading-unloading tests of carbon fiber reinforced aluminum laminates (CRALL) have been carried out in a tensile impact apparatus, and quasi-static tensile tests have been performed on a MTS-810 machine. Complete stress-strain curves of composite in the strain rate range from 0.001–1200 1/s have been obtained. Experimental results show that CRALL composite is a strain rate sensitivity material, the tensile strength and failure strain both increased with increasing strain rate. A linear strain hardening model has been combined with Weibull distribution function to establish a constitutive equation for CRALL. The simulated stress-strain curves from model are in good agreement with the test data. The analysis of the model shows that the Weibull scale parameter, σ0, increased with increasing strain rate, but Weibull shape parameter, β, can be regarded as a constant.

Deformation Behavior of Bellows Pipes for Laying Cables Under Ground by Axial Load and Bending Moment

Recently, electricity demand is rising steeply with advance of science. Additionally quantity of cables such as telephone and optical fiber is rising with communications development and increase of residence. These cables are untidily wired in the air with telephone pole. They impair cityscape and disturb pedestrian safety. Therefore improvement of procedures installing cables is requested. In order to solve it, the plan [1] which buries cables protected in pipes under ground is progressing. They are called buried pipes and consist of straight pipe made from stainless steel or plastic. However there is concern that the buried pipe is crushed and broken by the complex load due to earthquake and ground subsidence. Thus, it is necessary to develop the buried pipe with function of flexibly against damage or rupture. We focus attention to U-type bellows pipe with function of flexibly. In this study, we conduct tensile, compressive, bending test and numerical analysis of those tests using finite element method. From result, we investigate for the relationship between mechanical characteristic and deformation behavior. We study application of bellows pipe to buried pipe. In this study, we examined and analyzed deformation behavior when axial load and bending moment were given to specimens. Examinations items are as (1) we measured load, elongation bending radius by using are experimental device which modeled ground subsidence. (2) We obtained deformation behavior by numerical analysis by using constituted equations of solid mechanics. (3) We conducted simulation analysis of models constructed by finite element method. By comparing these three items, the deformation behavior is clarified.