Byung Chai Lee

Reliability-based design optimization using a moment method and a kriging metamodel

Reliability-based design optimization (RBDO) has been used for optimizing engineering systems with uncertainties in design variables and system parameters. RBDO involves reliability analysis, which requires a large amount of computational effort, so it is important to select an efficient method for reliability analysis. Of the many methods for reliability analysis, a moment method, which is called the fourth moment method, is known to be less expensive for moderate size problems and requires neither iteration nor the computation of derivatives. Despite these advantages, previous research on RBDO has been mainly based on the first-order reliability method and relatively little attention has been paid to moment-based RBDO. This article considers difficulties in implementing the moment method into RBDO; they are solved using a kriging metamodel with an active constraint strategy. Three numerical examples are tested and the results show that the proposed method is efficient and accurate.Reliability-based design optimization (RBDO) has been used for optimizing engineering systems with uncertainties in design variables and system parameters. RBDO involves reliability analysis, which requires a large amount of computational effort, so it is important to select an efficient method for reliability analysis. Of the many methods for reliability analysis, a moment method, which is called the fourth moment method, is known to be less expensive for moderate size problems and requires neither iteration nor the computation of derivatives. Despite these advantages, previous research on RBDO has been mainly based on the first-order reliability method and relatively little attention has been paid to moment-based RBDO. This article considers difficulties in implementing the moment method into RBDO; they are solved using a kriging metamodel with an active constraint strategy. Three numerical examples are tested and the results show that the proposed method is efficient and accurate.

GEOMETRICALLY NON-LINEAR AND ELASTOPLASTIC THREE-DIMENSIONAL SHEAR FLEXIBLE BEAM ELEMENT OF VON-MISES-TYPE HARDENING MATERIAL

A three-dimensional elastoplastic beam element being capable of incorporating large displacement and large rotation is developed and examined. Elastoplastic constitutive equations are applied to the beam element based upon the assumption of small deformational strain leading to a material formulation which is completely objective for the application of stress update procedures. The continuum-type equations of plastic model of J2 mixed hardening are transformed into the beam equations by satisfying beam hypotheses. An effective stress update algorithm is proposed to integrate elastoplastic rate equations by means of the so-called multistep method which is a method of successive control of residuals on yield surfaces. It avoids severe divergence when the displacement increments become large which is usual for the continuation methods. Material tangent stiffness matrix is derived by using consistent elastoplastic modulus resulting from the integration algorithm and is combined with geometric tangent stiffness matrix. Different from other elements, the present element is shear flexible and can satisfy the plasticity condition in a pointwise fashion. A great number of numerical examples are analysed and compared with the literature. The proposed beam element is verified to be not only quite accurate but also very effective for the analyses of pre-buckling and large deflection collapse of spatial framed structures.

The use of generalised deformation boundaries for the analysis of axisymmetric extrusion through curved dies

Abstract A generalised kinematically admissible velocity field is derived for axisymmetric extrusion through curved dies by employing rigid-plastic boundaries expressed in terms of arbitrarily chosen continuous functions. The corresponding upper-bound extrusion pressure is related directly to boundary functions for the plastically deforming region when the die shape, lubrication condition and material characteristics of the billet are given. The proposed method of analysis makes it possible to predict the deformation pattern as well as extrusion pressure. In computation a third-order polynomial is chosen for the die boundary and the bounding function for the plastic region is chosen to be a fourth-order polynomial. The workhardening effect is considered in the formulation. The plastic boundaries as well as stream lines are affected by various process parameters. The theory predicts the relatively faster axial flow at the center than near the die boundary for greater friction factor even with the same die shape. The effects of area reduction and die length are also discussed in relation to extrusion pressure and deformation. Experiments are carried out for steel billets at room temperature. Deformation patterns are measured for several area reductions by the photoetching technique and the extrusion pressure is measured using a load-cell. The predicted extrusion pressure is in excellent agreement with the value computed by the finite element method. The deformation patterns agree well with the experimental observation.

Efficient evaluation of probabilistic constraints using an envelope function

Probabilistic design optimization deals with uncertainties quantitatively and can be characterized by probabilistic constraints. As evaluating the probabilistic constraints requires quite large computational cost, reduction of the number of the probabilistic constraints by using an envelope function can improve the efficiency of the optimization process. Several numerical examples are tested adopting the reliability index approach and the performance measure approach with or without the envelope function. The results show that the proposed method requires fewer function evaluations. Efficiency improvement would be remarkable for large structural problems.

New stress assumption for hybrid stress elements and refined four-node plane and eight-node brick elements

A new stress assumption for hybrid stress elements is presented. Generalized incompatible modes are proposed and incorporated into the constraint equations for assumed stresses. The physical meaning of the resulting constraint equations is discussed. The present stress assumption, which can consider the mesh distortion more rigorously, is based on the physical interpretation of the role of the generalized incompatible modes and substantiated with simple mesh distortion measures defined in this paper. The stress assumption is adapted to the previous four-node hybrid stress element, 5β-I and the eight-node hybrid stress brick element, 18β, which results in a new four-node plane element, M5β and an new eight-node brick element, M18β. Numerical results show that the refined elements are noticeable in low sensitivity to mesh distortion and in high-accuracy of stresses.

Analysis of partly corrugated rectangular diaphragms using the Rayleigh-Ritz method

In this paper, the Rayleigh Ritz method is applied to static analyses of partly corrugated four-edges-clamped rectangular diaphragms. We use coupled variational equations (derived from the principle of virtual displacement), and describe some practical considerations needed to analyze multiregional diaphragms by the method. We approximate a sinusoidal corrugation by an equivalent flat single layer, and derive equivalent in-plane and bending stiffnesses using the theory of engineering mechanics. We demonstrate the effectiveness and usefulness of the present method through examples (in one example, we compare the calculated deflection with that obtained by a finite-element program). We examine a partly corrugated rectangular plate with residual stress, and investigate the effects of corrugation parameter variations. The analysis technique presented in this paper is very convenient, efficient, and reliable for analyzing seemingly difficult microelectromechanical system devices built on partly corrugated thin diaphragms with various residual stresses.

Prediction of bending collapse behaviours of thin-walled open section beams

Abstract Crushing behaviours of thin-walled open section beams are simulated using the simplified kinematic models. Systematic process of simulation is presented and applied to L-section and I-section beams. Basic processes can be conceptually divided into composition of mode shapes, location of deforming elements as a function of global process control parameter, calculation of plastic work done, estimation of mode parameters and calculation of crushing behaviours. A systematic numerical method is suggested to determine geometry and mode parameters according to the progress of collapse since it is generally very complicated to obtain closed form expressions for bending collapse problems. In the present method, mode parameters are determined by minimizing the plastic work done at very early stage of collapse, while it has been done conventionally by minimizing the mean crushing force. The results are in good agreement with those from finite element analyses and from the literature.

AN EFFICIENT PROFILE REDUCTION ALGORITHM BASED ON THE FRONTAL ORDERING SCHEME AND THE GRAPH-THEORY

Abstract A frontal ordering scheme is incorporated into the two step approach of finite element ordering. The algorithm involves ordering of the finite elements by the Cuthill-McKee algorithm and numbering of the nodes by a newly proposed scheme. The scheme is introduced for an efficient reduction of profiles of resulting stiffness matrices and is based on the concept of frontal ordering and the adjacency measure of the graph theory. A computer program is developed and many examples are tested. The results are compared with those of existing algorithms and demonstrate the efficiency and the reliability of the proposed algorithm.

Analysis and Simulation of the Failure Characteristic of a Single Leg Bending Joint with a Micro-Patterned Surface

The interface characteristic influences the strength of the adhesive joints. For this reason, there have been studies to improve the strength of the adhesive joints using various surface treatment methods. One of these methods, mechanical interlocking by surface roughness, has been known as an effective method but an analysis of the roughness effect is not easy because the roughness profile such as height, shape, and density of peaks and valleys by sandblasting, sandpaper or etching is random. In this paper, micro-patterns on a bonded surface of a steel substrate were fabricated then single leg bending joints with carbon fiber reinforced polymer (CFRP) and steel were manufactured by a co-curing process. The mechanical interlocking effect was analyzed with three-point bending tests of single leg bending joints. Experimental results show that the mechanical interlocking effect leads to material damage and energy absorption, and complicated failure characteristics occur due to the micro-patterned surface. A cohesive zone model was introduced to simulate the single leg bending joints with the micro-patterned interface. A finite element analysis was performed to predict the failure load and load-displacement curve of the single leg bending joints with the micro-patterned surface and numerical results were compared with the experimental results. Failure loads obtained by the numerical results predicted the experimental ones with a relative error of 10%.

Effect of Surface Roughness on the Adhesive Strength of the Heat-Resistant Adhesive RTV88

Heat-resistant adhesive RTV88 is a hyper-elastic material and so far there have been little research on using RTV88 in adhesive joints. In this study, the effect of surface roughness on the adhesive strength of RTV88 was examined. Aluminum adherends were first sandblasted in order to generate rough surfaces, and then tensile–shear tests on Al/RTV88 single lap joints were performed. The shear strength was shown to be influenced by surface roughness. Peel failure was dominant when the surface roughness was at a low level. However, cohesive failure was the major type of failure when the surface roughness was at a high level. Effective area, peel failure area, and cohesive failure area were introduced to explain the effects of surface roughness on the adhesive strength. An empirical relation for the failure force was proposed, based on these parameters. Tensile tests of the RTV88 bonding was performed in order to obtain the necessary data. Finally, the empirical relation for the failure force was verified by tensile–shear test results.