A finite element contact analysis algorithm has to pass the so-called patch test. In the conventional one-pass approach, the virtual work due to contact force is evaluated by concentrated contact force and corresponding virtual displacement. This means that the contact force at the contact surface between deformable bodies is not transmitted appropriately in the virtual work sense. This paper proposes a new algorithm based on the one-pass approach, which evaluates the virtual work due to contact force by integrating it on the contact surfaces. Furthermore, the nodal contact pressure in the master contact surface is transmitted from that in the slave contact surface by projecting the master node onto the slave element. In this way, the proposed algorithm is capable of correctly evaluating the equivalent nodal contact force and passing the contact patch test. Two numerical examples verify the effectiveness of the new algorithm.
In this paper a finite element method is presented to study the effects of delamination on free vibration characteristics of graphite-epoxy composite pretwisted rotating shells. Lagrange’s equation of motion is used to derive the dynamic equilibrium equation and moderate rotational speeds are considered wherein the Coriolis effect is negligible. An eight noded isoparametric plate bending element is employed in the formulation incorporating rotary inertia and effects of transverse shear deformation based on Mindlin’s theory. To satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front, a multipoint constraint algorithm is incorporated which leads to unsymmetric stiffness matrices. Parametric studies are performed in respect of location of delamination, fibre orientation, rotational speed and twist angle on natural frequencies of cylindrical shallow shells. Numerical results obtained for symmetric and unsymmetric laminates are the first known non-dimensional frequencies for the analyses carried out here.
A computational procedure for analyzing the deformation and fracture of solid polymers is developed based on a molecular chain model. In the model, the polymer solid is represented by a network of nonlinear elastic chains. Cellular automata modeling is employed to generate the network of polymer chains. Van der Waals and viscous forces acting on the chains are taken into account and are approximated to act at the nodal points of the network. A stiffness equation is derived by employing the principle of virtual work, in which geometrical nonlinearity due to a large deformation is considered. Slippage and scission of chains are also taken into consideration. The effects of molecular weight distribution and molecular chain scission due to UV-degradation are discussed.
Large-scale molecular dynamics simulations of tensile deformation of amorphous metals with nanocrystalline particles were performed in order to clarify the effects of particle size and crystal volume fraction on the deformation property and the strength. It was clarified that the size effects of the particle are very small, whereas the influences of the crystal volume fraction are large. Young’s modulus and the flow stress become large as the crystal volume fraction increases. Even after the yielding of the amorphous phase, the stress of the crystal phase still continues to increase. Thus, the flow stress of the composite increases after yielding, which prevents plastic localization and improves the ductility. When the crystal volume fraction is small, the stress distribution is homogeneous in the particle including near the amorphous-crystal interface. Therefore, possibility of deformation is small, and inside-particle plastic deformation is negligible. When the crystal volume fraction is high, the particle undergoes plastic deformation even with small global deformation. After the yielding of the crystal particle, the flow stress decreases because defects are introduced into the crystal. It is expected that there is an ideal crystal volume fraction that gives the maximum ductility. A Lennard-Jones potential modified to enforce the continuity at the cut-off distance was used as an interatomic potential. The potential parameters were defined based on Inoue’s three basic principles.
The purpose of the present study is to analyze the circuit connection reliability of printed wiring boards (PWBs) in relation to the thermal stresses obtained by FEM and to apply the FEM data to a data-mining method in order to clarify the factors that influence the thermal stress of the copper plating on the drilled hole walls. The following are the conclusions obtained herein: (1) Decreasing the thickness of the build-up layer is effective in reducing the thermal stress of the copper plating. (2) Using the data-mining method, new factors that were hidden in the data, such as the coefficient of thermal expansion in the Z direction, were revealed, despite the presence of other complex factors.
The stress intensify factor (SIF) of a surface crack having an undulated crack front, which was defined using a cosine function based on a semi-circular crack, was evaluated by finite element analysis. The average SIF along the crack front is almost the same if the area of crack is the same. Furthermore, crack growth simulations were conducted. The undulated front crack tended to become semi-elliptical in shape during growth. Although the undulated front crack takes a relatively small SIF compared with the semi-circular crack, the growth rate was faster. This incoherence was brought about by the difference in the crack front length.
In this paper, an analytical solution for an infinite strip having an eccentrically located circular hole is given when the strip is subjected to a pair of side pressures. The solution is based on an approach involving Papcovich-Neuber displacement potentials and deduced using the simple forms of Cartesian and cylindrical harmonics. The boundary conditions on both sides of the strip and around the hole are completely satisfied with the aid of the relations between the Cartesian and cylindrical harmonics. The solution is shown in a graph, and the effect of the eccentric hole on the stress distribution is clarified.
In the present work, the constitutive relations based on the combination of two back stresses are developed using the Armstrong-Frederick, Phillips and Ziegler’s type hardening rules. Various evolutions of the kinematic hardening parameter can be obtained by means of a simple combination of back stress rate using the rule of mixtures. Thus, a wide range of plastic deformation behavior can be depicted depending on the dominant back stress evolution. The ultimate back stress is also determined for the present combined kinematic hardening models. Since a kinematic hardening rule is assumed in the finite deformation regime, the stress rate is co-rotated with respect to the spin of substructure obtained by incorporating the plastic spin concept. A comparison of the various co-rotational rates is also included. Assuming rigid plasticity, the continuum body consists of the elastic deformation zone and the plastic deformation zone to form a hybrid finite element formulation. Then, the plastic deformation behavior is investigated under various loading conditions with an assumption of the J2 deformation theory. The plastic deformation localization turns out to be strongly dependent on the description of back stress evolution and its associated hardening parameters. The analysis for the shear deformation with fixed boundaries is carried out to examine the deformation localization behavior and the evolution of state variables.
In this paper, the behavior of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material layers subjected to an anti-plane shear loading is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with coordinate vertical to the crack. By using the Fourier transform, the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is the jump of the displacement across the crack surfaces. These equations are solved using the Schmidt method. The normalized stress, the electrical displacement and the magnetic flux intensity factors are determined for different geometric for the permeable electric boundary conditions. The relations among the electric filed, the magnetic flux field and the dynamic stress field near the crack tips can be obtained. Numerical examples are provided to show the effect of the functionally graded parameter and the thickness of the strip upon the stress, the electric displacement and the magnetic flux intensity factors of the crack.
In this paper, the non-local theory of elasticity is applied to obtain the dynamic interaction between two collinear cracks in functionally graded piezoelectric materials under the harmonic anti-plane shear stress waves for the permeable electric boundary conditions. To make the analysis tractable, it is assumed that the material properties vary exponentially with coordinate vertical to the crack. By means of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations that the unknown variable is the jump of the displacement across the crack surfaces. These equations are solved by use of the Schmidt method. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips. The non-local elastic solutions yield a finite stress at the crack tips, thus allows us to use the maximum stress as a fracture criterion. The finite stresses at the crack tips depend on the crack length, the distance between two cracks, the functionally graded parameter, the circular frequency of the incident waves and the lattice parameter of the materials, respectively.
Slip deformation in compatible bicrystal models with a tilted angle grain boundary subjected to tensile load is investigated using a finite element crystal plasticity analysis code. The accumulation of geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs) is studied in detail. Uniform deformation was expected to occur because the mutual constraint of crystal grains through the grain boundary plane does not occur in compatible bicrystals, but some results of the analysis show asymmetric deformation with the accumulation of GNDs near the grain boundary caused by the difference in strain hardening of slip systems, kink bands perpendicular to the primary slip direction and secondary slip bands parallel to the primary slip plane with accumulation of GNDs on the primary slip system in the form of bands. The mechanism of dislocation pattern formation in the bicrystals with a tilted angle grain boundary is discussed from the viewpoint of an imaginary disclination deformation field with pair body interaction.
This study proposes a MEMS microgripper design based on a compliant mechanism, utilizing the multi-input method to obtain greater output force and displacement. The compliant mechanism is very effective because the mechanism has flexible pieces that transmit force or deliver motion. The design domain is formed by the ground structure parameterization of the optimal topology. The goal is to obtain the optimal topology layout through computer simulation. This study combines insights from the topology optimization of the compliant mechanism and the piezoelectric microactuator to design a microgripper and to analyze outputs and displacement with different parameters under topology optimization.
Left ventricular wall motions during systole were investigated from a mechanical perspective by using a magnetic resonance tagging technique. Subjects were 7 patients with coronary artery bypass grafting (CABG). First, by analyzing strain in the left ventricular wall, cardiac contractility was evaluated in the patients with CABG. Next, by calculating displacement in the myocardial wall, paradoxical movements following CABG were quantitatively evaluated. Strain analysis showed local decreases in circumferential strain in 4 of 7 subjects. The results of displacement analysis clarified that following CABG, the degree of radial displacement was small in the septal wall and large in the lateral wall, and circumferential displacement towards the septal wall occurred in the anterior and posterior walls. Since this behavior was seen in both reduced and normal cardiac contractility groups, paradoxical movements in the present patients were not caused by reduced cardiac contractility, but rather by rigid-body motion of the entire heart.