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2025 Vol. 46, No. 2 Published: 2025-04-23

	162	Bi-mapping Solving Approach for the ICM Method of Structural Topology Optimization

		Based on the ICM (independent, continuous, mapping) method of structural topology optimization, a new approach for solving approach with bi-mapping is developed. Because the prefix “bi-” is abbreviated as B in English, it is called B-ICM approach. This approach consists of two steps: the first step is to apply L (linear) mapping to the structural topology optimization problem, making it a discrete model, and then construct the constraint function; the second step is to apply NL (nonlinear) mapping to the discrete model, making it a continuous model, and realizing the conversion of elemental topology variables from discrete to continuous. In the previous ICM method, the first step above only plays a theoretical derivation role, and the construction of constraint function, modeling and solving algorithms are included in the second step, so it belongs to the "one-step" approach. Although B-ICM belongs to the "two-steps" approach, the sequential dual quadratic programming algorithm commonly used in the ICM method is still adopted to solve the optimization model.The volume minimization problem with displacement constraints is taken as an example to illustrate the above modeling and solving process. The examples with single load case and multi-load cases confirm that the research achieves the expected results. Compared with the three methods aiming at obtaining clear topology (1, SIMP method with Heaviside projection; 2, Floating Projection Topology Optimization (FPTO) method; 3, Non-Penalized Smooth Boundary Material Distribution Topology Optimization (SEMDOT) method ) and the previous solving approach of the ICM method, the iteration times, clarity, optimization ability and other aspects are compared. The results show that the B-ICM solving approach performs best. This study not only enriches the modeling strategy of ICM method, promotes the improvement of solving approach of ICM method, but also provides a superior approach for solving blurry boundary problems. In the past topology optimization solving of continuum structure, the filtering operation adopted to eliminate the checkerboard and mesh dependence problems leads to blurry boundary of the optimal topology. And the larger the filtering radius, the more blurry the boundary.This paper overcomes the problem, and can successfully obtain the clear boundary of the optimal topology. It is worth mentioning that the key techniques of this study can be transplanted to all continuous variable optimization methods, including the variable density method.
		2025 Vol. 46 (2): 162-176 [Abstract] ( 9 ) HTML (1 KB) PDF (0 KB) ( 1 )

	177	Buckling and post-buckling of functionally graded sandwich nanoplates with surface effect

		Nanoplate structures are widely used in nanoelectromechanical systems because of their excellent mechanical properties. At the same volume, the specific surface area of the nano-laminates is much larger than that of the single-layer nanomaterials, and the surface effect is more significant. The influence of surface effect on nanostructures can be regarded as the combination of surface elasticity and surface residual stress. The classical plate-shell theory does not consider the surface effect and is no longer suitable for describing nanostructures such as nanoplate-shells. As a new type of composite materials, functionally graded materials have received more and more attention from researchers. The mechanical properties of micro/nano structural components made of functionally graded materials are completely different from the macroscopic structures made of conventional materials. Plate structure is a basic component in nano-electromechanical systems, so it is necessary to study the mechanical properties of plates made of functionally graded materials. In this paper, based on Kirchhoff plate theory and Mindlin plate theory considering shear deformation, the buckling and post-buckling behaviors of functionally graded sandwich nanoplates with surface effect are studied. Based on the force balance analysis, the governing equations of buckling and post-buckling are obtained. The analytical solutions of critical buckling loads under uniaxial and biaxial compression are given. By using Galerkin method, the approximate solutions of critical post-buckling loads under movable and immovable boundary conditions are given. Numerical results show that the influence of surface effects on the stability of functionally graded nano laminated plates is related to the volume fraction of the materials that make up the plates, as well as to the ratio of structural surface area to volume. Considering that shear deformation will reduce the critical load for buckling and post buckling of functionally graded nano laminated plates. For thinner nano laminated plates, the influence of shear deformation can be ignored.
		2025 Vol. 46 (2): 177-191 [Abstract] ( 8 ) HTML (1 KB) PDF (0 KB) ( 1 )

	192	Study on the Optimization of Elastic Isotropy of SLM Additive Manufactured 316L Steel Metamaterials

		Most existing isotropic metamaterial designs assume that the base material possesses isotropic symmetry. However, 316L steel produced by selective laser melting (SLM) typically exhibits mechanical anisotropy, which strongly depends on the manufacturing process and parameters. The limited experimental studies currently available are insufficient to fully reveal the elastic symmetry of 316L steel under different scanning strategies, and the quantitative impact of varying laser powers on Young's modulus remains unknown. In this study, ultrasonic resonance experiments were conducted to characterize the elastic constants of 316L steel under two typical laser scanning strategies (parallel and orthogonal scanning) and two laser power levels (214.2W and 274.2W). The results indicate that under the orthogonal scanning strategy, the symmetry of the steel degraded to transverse isotropy at a power of 214.2W, while the material remained orthotropic at a power of 274.2W, indicating that transverse isotropy results from specific laser power. Compared to orthogonal scanning, 316L steel produced using parallel scanning exhibited stronger anisotropy. Within the range of laser powers investigated, Young's modulus was found to be insensitive to power variations. Based on the experimentally obtained elastic constants and finite element simulations, we optimized the elastic isotropy of three types of truss metamaterials: FCC-BCC, SC-OT, and SC-OT-BCC, achieving shape control by adjusting rod dimensions. The optimization results showed that isotropic metamaterials made from SLM 316L steel and cast 316L steel possess nearly identical elastic properties. From an application perspective, this research offers feasible solutions to overcome the technical challenges of producing isotropic metamaterials using SLM additive manufacturing.
		2025 Vol. 46 (2): 192-205 [Abstract] ( 12 ) HTML (1 KB) PDF (0 KB) ( 1 )

	206	Perturbation method for solving tensile and compressive deformation of circular rod with axisymmetric rough surface

		Due to factors such as processing techniques, daily abrasion, and atmospheric corrosion, the surfaces of components typically exhibit a certain level of surface roughness. This paper primarily investigated the tensile and compressive deformation behavior of circular rods with axisymmetric random rough surfaces. First, a digital reconstruction of the rough circular rod model was conducted, where the rough surface was jointly characterized by two statistical parameters: the root mean square height and the correlation length. Then, the dimensionless governing differential equation for the tensile and compressive cases of the rough circular rod was derived through the infinitesimal element method. Subsequently, in combination with the perturbation method and the fast Fourier transform, the governing equation was solved, obtaining the perturbation solution for the tensile and compressive deformation of the rough circular rod. The validity of the perturbation solution was verified by comparison with the analytical solution and the finite element solution. Finally, in order to explore the influence of the statistical parameters of rough surfaces on tensile and compressive deformation, the contributions of the first-order and second-order perturbation solutions to the results were systematically compared, and an empirical formula for the perturbation amplitude was established. The influence of perturbation on the results gradually increases with the increase of the root mean square height and the correlation length; the proportion of the second-order perturbation solution in the perturbation grows with the increase of the root mean square height, while it is not affected by the correlation length. This work not only expands the research scope of traditional problems in mechanics of materials related to tensile and compressive, but also provides an example of the application of mathematical and physical methods in mechanical practice. Moreover, this study offers a theoretical basis for optimizing the manufacturing processes of components and quantitatively assessing the impact of surface defects on the mechanical properties of components.
		2025 Vol. 46 (2): 206-217 [Abstract] ( 12 ) HTML (1 KB) PDF (0 KB) ( 1 )

	218	Investigation on Quasi-static Fracture Propagation of Dissimilar metal welds in Special Vehicles at Different Temperature

		Dissimilar metal welding parts in special vehicles equipment are the key parts that affect their performance, and different working environment temperatures also have different effects on the fracture behavior of cracks. In order to study the effect of temperature on quasi-static crack propagation in dissimilar metal welds, this paper combined the finite element of crack tip propagation and the interaction integral under thermal load and the simulation method of quasi-static crack propagation path at different temperature. Compared with the analytical solution, the correctness of the method and the region independence of the integral are proved. The research in this paper is of great engineering significance for the performance prediction of special vehicles.
		2025 Vol. 46 (2): 218-229 [Abstract] ( 26 ) HTML (1 KB) PDF (0 KB) ( 1 )

	230	Physics information neural network method for solving plane stress problems

		This article proposes a method for solving plane stress problems based on Physical Information Neural Network (PINN). Firstly, inner and boundary particles are randomly generated in the solution domain [x, y]. Then, the geometric equations, constitutive equations, equilibrium equations, and boundary condition physical constraints of inner particles in the plane stress problem are introduced into the loss function of the neural network model, making the model physically meaningful. By minimizing the loss function, it approximates the solution of partial differential equations (PDEs). It can be seen that this method does not involve the process of grid partitioning, only the process of optimizing and training the loss functions of inner and boundary particles. Therefore, the PINN method is essentially a meshless method that can solve the shear locking problem caused by mesh partitioning in traditional finite element plane stress analysis. Subsequently, the feasibility and effectiveness of the proposed method were verified by comparing the finite element method (FEM) through numerical examples. The analysis of the calculation results shows that the PINN method can solve plane stress problems without the need for any label data, as well as solve the finite element defect of shear locking caused by false shear deformation in the finite element model due to mesh division.
		2025 Vol. 46 (2): 230-243 [Abstract] ( 13 ) HTML (1 KB) PDF (0 KB) ( 1 )

	244	Buckling Analysis and Experimental Validation of Extension-twist Multicoupled Laminates

		When the extension-twist multicoupled laminate is used to construct a bending-twist coupling structure, the panel on the inside of the bend will be subjected to compressive load, and buckling instability will occur when the compressive load reaches a critical value, which weakens the bearing capacity of the structure. Therefore, in order to improve the theoretical basis of the design of the bending-twist coupling structure, the analytical solution of the critical buckling load of the four-sided simply supported extension-twist multicoupled laminate under in-plane compressive load was obtained by using the double triangular series method. With the maximum buckling load and coupling effect as the optimization objectives, a multi-objective optimization design model based on the weight coefficient method was established, and the sequential quadratic programming method (SQP algorithm) was used to complete the optimization, and the laminate with greater coupling effect and bearing capacity was designed. Based on the layup law of the optimal laminate, the numerical simulation verification and robustness analysis of the buckling analysis model were completed. The analysis results show that the deviation between the analytical results and the simulation results of the buckling load of the laminate is within 5%. This method has high accuracy and provides a new idea for the buckling analysis of composite laminates. Finally, the multi-directional loading testing machine was used to complete the experimental measurement of the buckling load of the tensile torsion-multi-coupling effect laminate laminates, and the error between the measured value and the theoretical value was within 3%, which verified the correctness of the theory.
		2025 Vol. 46 (2): 244-256 [Abstract] ( 9 ) HTML (1 KB) PDF (0 KB) ( 1 )

	257	A new type of non-probabilistic convex model for structural uncertainty analysis

		The non-probabilistic convex model only requires the boundaries of structural uncertain parameters and is suitable for dealing with engineering problems with limited samples. However, the available convex models focus mainly on regular mathematical models, and thus may provide the excessive expansion of the uncertainty domain. In view of this, in this paper a new type of convex model, namely an interval and ellipsoidal intersection model, is proposed to bound the uncertainty domain, whereby the corresponding structural uncertainty propagation analysis method is investigated. Firstly, the interval and ellipsoidal intersection model is proposed to describe the uncertain domain, which can be constructed by taking the intersection of the interval model and the ellipsoidal model. Subsequently, the proposed model is applied to structural uncertainty propagation analysis, and two cases of the nonlinear response function are considered. For the weakly nonlinear response function, its linear approximation can be obtained by using the first-order Taylor series expansion, and then a semi-analytical method is developed to predict its structural response interval. For the strong nonlinear response function, its nonlinear approximation can be obtained by using the second-order Taylor series expansion, and then the Sequential Quadratic Programming (SQP) method is adopted to predict its structural response interval. Finally, the results from four numerical examples indicate that the proposed model generally offers a smaller volume of the uncertainty domain and a narrower structural response interval than the interval and ellipsoidal models; and the semi-analytical method has a higher efficiency than the Sequential Quadratic Programming (SQP) method and the Monte Carlo Simulation (MCS) method.
		2025 Vol. 46 (2): 257-274 [Abstract] ( 9 ) HTML (1 KB) PDF (0 KB) ( 1 )

	275	Distance-minimizing data-driven method for solving structural dynamic response

		As a new paradigm of computational mechanics, distance minimizing data-driven method has significant advantages in predicting structural mechanics behavior. This method directly inputs the discrete material datasets (a set of stress-strain pairs), bypasses the conventional empirical constitutive modeling. The boundary value problem is solved by defining the distance functional from the solution set to the material dataset, and searching the functional extreme value from the material dataset to satisfy the strain-displacement relationship and the equilibrium equation. The distance minimizing data-driven method has been successful in solving undamped vibration problems, but it cannot be used for damped vibration problems. This study adopts the structural dynamic equilibrium equation with damping term as the constraint condition of the distance functional, uses the final value at the previous time step as the initial value at the current time step to replace the random initial value scheme, proposes a distance minimizing data-driven method for solving the structural dynamic response. Taking single-degree-of-freedom system and multi-degree-of-freedom truss as examples, the effectiveness and efficiency of the proposed method are verified by the dynamic response analysis of linear and nonlinear materials.
		2025 Vol. 46 (2): 275-285 [Abstract] ( 8 ) HTML (1 KB) PDF (0 KB) ( 1 )

	286	A Study of Geometric and Material Distortion Scale Model of the Free Vibration of Shallow Spherical Shells

		This study addresses the design of geometric and material distortion scale models for the free vibration of large thin-walled shallow spherical shells. By applying similarity transformations to the frequency equation and natural frequency solutions of clamped shallow spherical shells, we derive the similarity conditions for free vibration and the scaling law for natural frequencies. Numerical simulations verify the accuracy of the frequency formula, similarity conditions, and scaling laws for natural frequencies of shallow spherical shells under various rise-to-thickness ratios. The research findings demonstrate that the theoretical frequency formula is consistent with the simulation results for shallow spherical shells under different rise-to-thickness ratios. Models designed according to these similarity conditions, combined with the scaling laws, can accurately predict the natural vibration characteristics of the prototype. The similarity conditions and scaling laws presented in this study can provide valuable references for the design and experimentation of scaling models with thickness and material distortions.
		2025 Vol. 46 (2): 286-296 [Abstract] ( 6 ) HTML (1 KB) PDF (0 KB) ( 1 )

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