• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.35 no.6
• /
• pp.367-374
• /
• 2022

This papter presents the use of the automatic differential method based on the backpropagation method to obtain the design sensitivity and its application to topology optimization considering the stress constraints. Solving topology optimization problems with stress constraints is difficult owing to singularities, the local nature of stress constraints, and nonlinearity with respect to design variables. To solve the singularity problem, the stress relaxation technique is used, and p-norm for stress constraints is applied instead of local stresses for global stress measures. To overcome the nonlinearity of the design variables in stress constraint problems, it is important to analytically obtain the exact design sensitivity. In conventional topology optimization, design sensitivity is obtained efficiently and accurately using the adjoint variable method; however, obtaining the design sensitivity analytically and additionally solving the adjoint equation is difficult. To address this problem, the design sensitivity is obtained using a backpropagation technique that is used to determine optimal weights and biases in the artificial neural network, and it is applied to the topology optimization with the stress constraints. The backpropagation technique is used in automatic differentiation and can simplify the calculation of the design sensitivity for the objectives or constraint functions without complicated analytical derivations. In addition, the backpropagation process is more computationally efficient than solving adjoint equations in sensitivity calculations.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.7
• /
• pp.2087-2096
• /
• 1996

Recentrly advantages in composite and light weight material techniques have led to the increased use of bonded dissimilar materials such as ceramics/metal bonded joints, IC package, brazing, coating and soldering in the various industries. It is required to analyze the evaluation method of fracture strength and design methodology of bonded joints in dissimilar materials. Stress singularity according to changes of scarf angles for bonded scarf joints in dissimilar materials was investigated by the boundary element method and static experiments. In this paper, effect of the stress singularity factors at the interface edges of scarf joints on various dissmilar materials combinations were investigated by analysis of its stress and stress singularity index using 2-dimensional elastic program of boundary element method. And the variations of stress singularity index by changes for Young's modulus ratios of materials and scarf angles were investigated. Also, it is found that stress singularities at bonded interface edges are disappeared for certain combination of scarf angle in a pair of bonded dissimilar materials. As the results, it is proposed that the strength evaluation by using stress singularity factors, $\Gamma$, considering stress singularity at the interface edges of bonded dissimilar materials, is very useful.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.1
• /
• pp.135-145
• /
• 1996

Order of stress singularities at bonded Edge Corners with two or three dissimilar isotropic Materials is analyzed. The problem is formulated by Mellin transform and characteristic equation is obtained as a determinant of matrix considering boundary conditions. Roots of characterictic equation are determinde by numerical calculations with ward method, from which the order of stress sigularities is obtained. Applying the results to the electronic packaging, the order of stress singularities is obtained. Applying the results to the electronic packaging, the order of stress singularities at bounded edge corners is calculated as a various bouned edge angle with given material combinations. Comparing the results, the optimal material combinaitons of bounded edge corners and bouned edge angle to reduce stress singularity could be determined. It suggests that the results are used to the basic design of electronic packaging reducing the stress singularity.

• Journal of the Korean Society for Precision Engineering
• /
• v.9 no.2
• /
• pp.108-115
• /
• 1992

이종재료의 접합면에 수직으로 존재하는 크랙에 대하여 경계요소 해석을 수행하여, 그 결과 실용가능한 수치 근사해을 얻을 수 있었다. 크랙을 정확히 모델링하기 위하여 크랙표면을 분리영역으로 하는 영역분할법을 채택하였으며, 해의 정확성을 향상시키기 위하여 등매개 2차요소로의 경계분할과 함께 크랙선단에서 표면력의 특이성을 나타내도록 하였다. 응력확대계수는 크랙표면상 절점의 상대변위를 이용하여 결정하였다. 또한 이종 재료내 크랙에 대하여 응력확대계수를 간단히 구할 수 있는 간편해석법을 제안하고 이의 적용 가능한 범위를 제 시하였다.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.14 no.4
• /
• pp.59-67
• /
• 2006

Recently, application of friction welded SUH35/SUH3 is increasing in the manufacturing process of automotive engine valves For securing its reliability and a reasonable strength evaluation method, it is necessary to assess stress singularity under the residual stress condition on the friction welded interface between dissimilar materials. In this paper, strength evaluation method of friction welded materials was investigated by boundary element method and static tensile testing. An advanced method of quantitative strength evaluation for SUH35/SUH3 friction welded material is to be suggested by establishing fracture criterion by using stress singularity factors.

• Journal of Ocean Engineering and Technology
• /
• v.17 no.6
• /
• pp.72-76
• /
• 2003

This paper deals with the stress singularity developed in a polymer layer that is coated to a concrete surface, due to temperature change. The boundary element method is employed to investigate the behavior of interface stresses. The polymeric layer is assumed to be a linear viscoelastic material, and is thermorheologically simple. The order of the singularity is obtained, numerically, for a given viscoelastic model. Numerical results exhibit the relaxation of interface stresses, and large gradients are observed in the vicinity of the free surface. Results show that the stress singularity factor is relaxed with time, while the order of the singularity increases with time for the viscoelastic model.

• Computational Structural Engineering
• /
• v.9 no.1
• /
• pp.77-83
• /
• 1996

The overall stress intensity factor for edge crack located at the interface between fiber and matrix of a unidirectional graphite/epoxy laminate model subjected to a transverse tensile strain have been computed using the boundary element method. Such crack might be generated due to a stress singularity in the vicinity of the free surface. The amplitude of complex stress intensity factor has the constant value at large crack lengths.

• Journal of the Korean Geotechnical Society
• /
• v.17 no.3
• /
• pp.25-32
• /
• 2001

보편적인 탄소성 캡 모델은 전통적인 등방 이론에 기초를 두고 있다. 이러한 모델의 응력적분 및 접선 계수의 유도는 여러 가지 논문들에 나타나 있지만 축차 및 체적 거동을 동시에 다루는 내제적인 해석법을 통한 지반해석은 아직까지는 많은 도전이 요구되고 있다. 앞선 동반 논문에서는 비연속적으로 연결된 항복면 사이의 접선 계수는 특이점이 됨을 나타내었고 이에 대하여 새로운 캡 모델의 구성식이 제시되었다. 본 논문에서는 제시된 캡 모델의 비 조건적이고 안정된 내재적 응력적분 및 일관된 탄소성 접선계수를 유도하였다. 또한 간단한 예제를 통하여 모델의 수행능력을 보여주었고 사면안정계산이 수행되었다.

• Proceedings of the KSME Conference
• /
• 2001.11a
• /
• pp.234-239
• /
• 2001

The stress intensity factors have been widely used in numerical studies of crack growth direction. However in many cases, omissive terms of the series expansion are quantitatively significant, so we consider the computation of such terms. For this purpose, we used the finite element method with isometric quadratic quarter-point elements. For examples, infinite square plate with a slant crack subjected to a uniaxial load is analyzed. The numerical analysis were performed for the wide range of crack tip element lengths and inclined angles. The numerical results obtained are compared with the theoretical solutions. Also they were accurate and efficient.

• Proceedings of the KSME Conference
• /
• 2001.11a
• /
• pp.384-388
• /
• 2001

The higher order singularities[1] are systematically examined, and discussed are their complementarity relation with the nonsingular eigenfunctions and their relations to the configurational forces like J-integral and M-integral. By use of the so-called two state conservation laws(Im and Kim[2]) or interaction energy, originally proposed by Eshelby[3] and later treated by Chen and Shield[4], the intensities of the higher order singularities are calculated, and their roles in elasticplastic fracture are investigated. Numerical examples are presented for illustration.