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2014 Vol. 35, No. 4
Published:
325
Study of the coupled discretization of quadratically consistent meshfree and finite element methods
A coupled discretization scheme of meshfree methods using second-order basis and quadratic finite elements is proposed in the framework of continuous blending method (CBM). An additional node on the center of each edge on the boundary is introduced in the proposed scheme such that the essential boundary conditions can be straightforwardly enforced as in the finite element method. The Galerkin weak form is numerically integrated by the quadratically consistent 3-point (QC3) integration method. In comparison to the Nitsche's method originally used in QC3 to enforce essential boundary conditions, the proposed scheme does not introduce additional terms into the weak form and no artificial parameters are involved. In addition, numerical results also show that the accuracy of the QC3 method is further improved by the proposed coupled scheme.
2014 Vol. 35 (4): 325-333 [
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334
THE DISCUSSION ON EQUIVALENT TRANSVERSE SHEAR MODULUS OF HONEYCOMB CORES
The equivalent in-plane elastic moduli of hexagonal honeycombs have determinate solution. Compared to the in-plane properties, only the lower and upper bounds are obtained for equivalent transverse shear modulus. Due to the lack of determinate solution, it will bring many troubles for practical engineering applications. For this reason, this paper deals with the calculation of the transverse shear modulus of a honeycomb sandwich panel, under the influence of the thin face panel. Based on the Y-shaped representative unit cell, then the upper bound of hexagonal honeycomb is obtained when the ratio of the thickness of central wall to inclined wall is 1:1 and 2:1. The result shows that it is equal to the lower limit of Gibson and Kelsey’s formula. Finally, both the experimental data and finite element analysis show that the proposed theoretical solution can predict the equivalent shear modulus of honeycomb cores with good accuracy.
2014 Vol. 35 (4): 334-340 [
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212
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341
Multiple materials layout or material and structural system optimization
To solve the problem of multiple materials layout or material and structural system optimization, a new bi-directional evolutionary structural optimization method utilizing material interpolation scheme with penalization is proposed in this paper. Several classic examples are shown that the present BESO method can be used for the multiple materials layout or material and structural system optimization which the traditional BESO can not be solved. Number of practical significance conclusions are given by the important parameters researched. Computer program software for the new BESO program is built on the FEA software of ABAQUS and the post-processor package in MATLAB. This program is easy to use for engineers who may not be familiar with either FEA and structure optimization. And the developer can give a deep research on the algorithm by change the MATLAB.
2014 Vol. 35 (4): 341-346 [
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208
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347
The Plastic Buckling Critical Radius Model of The Cylindrical Shell Subject to Pure Bending
The critical curvature-radius as the main straightening technical parameter, decides the structure of equipment and the quality of products for straightening thin-walled tubes with equal curvature, however, it is usually carried out based on the experiential data and chart by skilled labourers, whose art is based on long experience and experiments, the special mathematical model of the critical radius is immediately necessary. But during mechanical modeling and analyzing, it is the critical curvature-radius that the cylindrical shell with the initial curvature under pure bending occurs plastic buckling, therefore, applying the general strain-displacement relations of the shell of revolution, the plastic buckling critical bending-moment model of the cylindrical shell under pure bending is presented by the Ritz method, based on the J2 deformation theory and energy method, then the critical radius is subsequently obtained and it is also shown how to solve synchronously. In order to certify whether it is correct, we have done some dynamic simulations by ANSYS/LS-DYNA, the results have shown that the model is approximate correct, by the comparison of the results of the simulations it is shown that wrinkling on the compression side of the cylindrical shell occurs before buckling due to ovalisation when the cylindrical shell occurs plastic buckling subject to pure bending.
2014 Vol. 35 (4): 347-356 [
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306
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357
Researchs on the Acceleration of Structure Eigenvalue Problem based on H – Matrices
The Hierarchical Dual Reciprocity Method (H - DRM) is proposed, which is applied for accelerating Dual Reciprocity Boundary Element Method (DRBEM) procedure and save computer memory during computation. Through applying low rank approximation with Adaptive Cross Approximation (ACA) algorithm for admissible blocks, the computer memory consumption will be saved significantly, and the scale of data involved in computation will diminish greatly. With respect to the different requirement about efficiency and scale, two different evaluation strategies are proposed --- pure hierarchical matrices method (PHDM) and mixed hierarchical matrices method (MHDM) --- to improve effect of H - DRM. Some numerical examples are presented in the last section for validation effect of the proposed methodology.
2014 Vol. 35 (4): 357-366 [
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203
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367
Nonlinear dynamical behaviors of torsional elastic support shallow arch under external excitations
The nonlinear dynamics of the hinged-hinged shallow arches with torsional springs constrained at both ends in case of 1:1 internal resonance under external excitation are investigated. The dimensionless dynamic equations are achieved by introducing the basic assumptions of shallow arch. Then by removing the damper, external load and non-linear terms, the obtained linear equation and corresponding boundary conditions are used to determine the frequencies and modes which take the torsional springs into account. Two internal resonance types of crossing and veering are found when the torsional constraints adopt different stiffness values. Further, the dynamic equation was performed by a full-basis Galerkin discretization and the multiple scale method was used to study the internal resonances by perturbation analysis, which leads to both the polar- and Cartesian-form averaging equations whose coefficients have a one-to-one correspondence with the stiffness of torsional spring. The numerical results for 1:1 internal resonance between the two lowest modes show the nonlinear interactions can be excited by external excitation. Moreover, when the parameters are controlled in a certain range there have periodic, quasi-periodic and chaotic windows in the system, and it enters into chaos by the (inverse) period-doubling bifurcation.
2014 Vol. 35 (4): 367-377 [
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227
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378
A new structural non-probabilistic reliability analysis method
Abstract: In order to handle the structural reliability problem with less test data effectively, a new structural non-probabilistic reliability method is proposed. In this method, the uncertainty of interval arithmetic structural non-probabilistic reliability calculation of nonlinear systems is taken into account, and then the universal grey numbers are used instead of the intervals parameters related to the structure to participate in the reliability calculation, which has overcome the impact of the interval arithmetic uncertainty on the reliability results. Through three numerical examples indicate that the proposed method has obtain smaller reliability results than the non-probabilistic reliability method based on interval when the interval arithmetic uncertainty existed, this is because the uncertainty of interval arithmetic is not considered in the latter method. The method proposed can obtain less conservative results. What’s more, it also can be more objectively and truly reflect the actual safety condition of the structure, and more suitable for engineering application.
2014 Vol. 35 (4): 378-383 [
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191
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384
Refined zig-zag theory for thick composite beams and finite element analysis
Zig-zag theory is widely studied and used as continuity conditions of transverse shear stresses are a priori satisfied. However, some problems will be involved in the zig-zag theory. The C1 shape functions have to be required during its finite element implementation, so that it is difficult to construct higher-order element based on the zig-zag theory. Moreover, previous zig-zag theories are less accurate in comparison with three-dimensional elasticity solutions. If these problems are neglected, some improper conclusions might be drawn as these zig-zag theories are used to analyze the mechanical problems of laminated composites. By proposing an accurate C0-type zig-zag theory considering transverse normal strain, difficulties encountered by previous zig-zag theories will be overcome in this paper. Based on the proposed zig-zag theory, a three-node beam element is constructed to verify the performance of the proposed model.
2014 Vol. 35 (4): 384-390 [
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206
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391
ANALYSIS OF THERMAL CREEP STRESS EVOLUTION AROUND MICRO-INTERFACIAL REGIONS IN THERMAL BARRIER COATINGS
The creep property of different interfaces in thermal barrier coatings(TBCs) under thermal cyclic loads is a key factor affecting residual stress around micro-interfacial regions, and it contributes to improve TBCs’ stability to explore the relationship between creep and residual stress in TBCs. With the usage of Norton creep model, a four-layer geometric model, consisting of a ceramic layer, an oxide layer, an adhesive layer and a substrate, is established based on thermal elastic-plastic creep theory to study stress evolution law around micro-interfacial regions in TBCs under thermal cyclic loads, in which the number of creep layers and the creep levels are included. Results show that changes in creep parameters and the number of creep layers affect the magnitude and distribution of interfacial residual stress in TBCs, which is of guiding significance on failure prediction of TBCs.
2014 Vol. 35 (4): 391-399 [
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194
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400
STUDY ON SOLDER/IMC INTERFACE DELAMINATION OF PBGA BASED ON CZM METHOD
In the reliability analysis of PBGA, Cohesive zone model (CZM) was introduced to study the interface delamination crack between solder and IMC of PBGA under thermal cycling through ANSYS software. The simulation considered the influence of Intermetallic compounds (IMC) which produced between the interface of SnAgCu solder and copper in the process of encapsulation. The results show that the solders of electronic packages under the higher stress and strain in the thermal cycling, and the outside of solders which far from the center under bigger stress and strain than the inside ones. The existence of IMC greatly reduced the reliability of solder. Interface delamination crack occurred at two ends of the interface between IMC and solder in the outside of the solder joints, and gradually extended to the interior with the increase of cycles. In front phases of the thermal cycles, the maximum damage on each interface increased quickly, and tended to be stable gradually with the increase of cycles. The damage of interface of the NO.4 solder is always the biggest in the whole process.
2014 Vol. 35 (4): 400-409 [
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418
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410
Research on stress-relaxation behavior of silicon-manganese alloy torsion-spring
The stress-relaxation test device is designed for rectangular section torsion spring and more group high-temperature tests are completed. The movable dislocation density function is proposed, and combined with the existing stress-relaxation dislocation theory, a new stress-relaxation kinetic equation is proposed for silicon-manganese alloy spring-steel. By using CREEP subroutine, ABAQUS secondary development interface, the new stress-relaxation kinetic equation is converted to a modified time hardening creep model based on implicit finite element method. Meanwhile, the torsion stress-relaxation behavior of silicon-manganese alloy spring-steel under 400°C is numerically simulated by using the new model. The simulating results showed that the stress-relaxation model is identical with the test results. The law of Von Mises stress on the surface of torsion-spring varying with time is consistent with that of the torque in the experiments.
2014 Vol. 35 (4): 410-416 [
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245
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