Analysis and Exploration of Topology Optimization Based on Variable Density Method

In this study, a topology optimization method based on combined mechanical analysis and variable density is presented for a large-scale casting structure with complex thin-walled structures. First, the mechanical analysis model of the frame is established, the first-order bending and torsional modes and stiffness values of the all-cast aluminum frame are obtained, and the basic mechanical parameters such as bending/torsional mode and stiffness constraints needed for topology optimization are defined. Using the variable density method, unneeded material that can be removed from the casting structure is identified. According to the design requirements, the optimization objective function and constraint conditions are established, and the variable density method is used to solve the problem. Analysis of the mechanical results before and after topology optimization reveals that the modes and stiffness values are larger than the target values, and the mass of the frame is reduced by 10.2 kg (i.e. 13.9%) compared with the original design. The application of the combined mechanical analysis and variable density method to a casting structure can effectively achieve lightweight design.

In the Formula Student Racing Car, the frame is a fundamental component that supports the body. The frame’s anti-deformation ability will impact the four-wheel positioning parameters of the car, which subsequently affect the car’s stability. The quality of the frame directly determines the power and efficiency of the racing car, making the frame crucial to the overall race performance. Therefore, researching lightweight frame design is particularly important to enhance frame performance and reduce its total weight. In this paper, based on the variable density method, the global topology optimization of the frame is carried out to obtain the distribution of the frame material, realize the efficient utilization of the material, and improve the torsional stiffness of the frame. Compared with the previous local topology optimization, the global topology optimization involves a wider range, and the results are more accurate. Based on the adjoint variable method, the sensitivity analysis of the frame is carried out to obtain the influence level of each design variable. The size of the frame is optimized according to the variables with high influence levels. After optimization, the total mass of the frame is reduced by 12.8%; the performance in terms of maximum displacement and maximum stress is improved; and the lightweight design of the frame is realized as a whole.

Topology optimization design of the main structure of 6-DOF manipulator based on the variable density method

For the lightweight design of composite sandwich corrugated structures, a new topology optimization design scheme is proposed using the variable density method. Multi-working conditions static analysis of the composite sandwich corrugated structure is carried out by finite element software. Then, the topology optimization is carried out by using the minimum flexibility method. Finally, the results of different working conditions are coupled to propose a new composite sandwich corrugated structure. The results indicate that the structure has a weight reduction of 34% and exhibits periodicity and continuity while also meeting the necessary mechanical properties to fulfill the engineering requirements. The optimization of composite sandwich corrugated structures has been achieved, providing a new approach to the lightweight design of composite sandwich structures.

Structural topology optimization is a crucial approach for achieving lightweight design. An effective topology optimization algorithm must strike a balance between the objective functions, constraints, and design variables, which essentially reflects the symmetry and tradeoff between the objective and constraints. In this study, a topology optimization method grounded in load path theory is proposed. Element bearing capacity is quantified using the element birth and death method, with an explicit formulation derived via finite element theory. The effectiveness in evaluating structural performance is assessed through comparisons with stress distributions and topology optimization density maps. In addition, a novel evaluation index for element bearing capacity is proposed as the objective function in the topology optimization model, which is validated through thin plate optimization. Subsequently, sensitivity redistribution mitigates checkerboard patterns, while mesh filtering suppresses multi-branch structures and prevents local optima. The method is applied for the lightweight design of a triangular arm, with results benchmarked against the variable density method, demonstrating the feasibility and effectiveness of the proposed method. The element bearing capacity seeks to homogenize the load distribution of each element; the technique in this study can be extended to the optimization of symmetric structures.

In this work, the topology optimization of a mortar base plate is analysed under impact loading conditions. Usually, in this case, only ordinary topology optimization under volume constraints is considered. However, to reduce the quality of the mortar base plate and facilitate engineering applications, the topological optimization problem of the continuum of the base plate under the engineering and quality constraint is considered. A finite element model has been established and verified by testing for the mortar base plate. The variable density method was used to obtain the topological optimization results of the base plate based on the force transmission path, and then the structure was reconstructed. The mass of the optimization model of the base plate is 12.78% lower than that of the original model. In comparison with the original base plate before optimization, the results show that the maximum deformation and stress of the base plate decreased by 16.85% and 35.52%, respectively. Also, the firing stability of the mortar meets requirements, which not only meet the design requirement but also provide a reference for the performance improvement and structural optimization design of the base plate.

The design of stiffeners is an effective approach to enhance the stiffness of panel-type structures. However, the stiffness–mass efficiency depends largely on the spacing, orientation, and cross-section of the stiffeners. In order to improve the stiffness–mass efficiency, this article presents a combined use of topology optimization and finite element analysis to the dynamic design of stiffeners for a typical panel. Finite element models of a flat and a stiffened rectangular panel were constructed. Modal analysis was conducted on the two panels to obtain the basic dynamic properties. Topology optimization model of the stiffened panel, so-called initial structure, was built based on the variable density method. According to the loading case and the predominant mode of the system, the objective function was determined to maximize the fundamental frequency of the panel. The stiffeners were chosen as the design domain. Optimal material density distributions of the stiffeners were obtained at different mass fraction. The finite element model of the optimal stiffened panel was built to reanalyze the dynamic properties and responses. An increase in the relative rate of change in the fundamental frequency versus mass was observed between before and after the optimization.

In allusion to a certain kind of bracket of work cabin overhead support equipment components of the special vehicle, taking OptiStruct software as optimization design platform, the topology optimization of the bracket is carried out by using variable density method. The geometry model of the bracket is rebuilt and the finite element analysis of the bracket is carried out, then the stress and deformation of before and after optimization are compared. The results show that the topology optimization method is an effective optimization method to carry out topology optimization of mechanical loading structure with FEA method. The model and approach adopted in this paper provide an important design reference to the mechanical structure and components lightweighting design.

Structural design of stamping die of advanced high-strength steel part for automobile based on topology optimization with variable density method

In order to optimize the structure of the pick cutter under the premise to meet its performance, and to achieve their own weight, the pick cutter of the longitudinal axis roadheader, which works under complicated seam conditions, is regarded as the research object.Based on the finite element method, statics strength analysis and fatigue life analysis of pick cutter are finished.According to the analysis results, the arbor of pick cutter is regarded as the object for topological optimization based on the variable density method.For the optimized structure, the necessary analysis is finished to verify its strength and fatigue life.The result shows that the optimized pick cutter satisfies the requirements with 24% weight reduction.It provides some reference for structure design, improvement and further research of pick cutter, and has a high guidance and practical value.

Aiming at the problem that large-scale ultra-high-pressure pneumatic ball valves opened and closed at large explosion instantaneously are prone to fatigue failure due to dynamic stress concentration under transient impact loads, this study proposes a multi-physics field coupling structural strength optimization design method based on finite element method. A transient dynamic model is constructed through an explicit dynamics algorithm to simulate the dynamic response under high-frequency impact loads during the blasting opening and closing process. Fluid-Structure Interaction (FSI) is introduced to analyze the interaction between fluid impact force and structural deformation. At the same time, the elastic modulus degradation effect of tungsten carbide/nickel-based alloy composites caused by frictional heat is considered, and the wear rate is calculated based on the wear model Archard. Secondly, the variable density method is used to perform topological optimization on the key areas of the valve body (such as the contact surface between the sphere and the valve seat), the internal rib layout is reconstructed to reduce stress concentration, and geometric parameters such as the valve seat inclination angle and the sphere diameter are screened. The nondominated sorting genetic algorithm (NSGA-II) is used to achieve the coordinated optimization of the leakage rate and the coating’s wear resistance and structural strength. By building an ultra-high pressure burst test bench, this paper combines strain gauges and high-speed cameras to verify the accuracy of the model and corrects the simulation boundary conditions based on the Kalman filter algorithm. The experiment shows that after optimization, the maximum equivalent stress peak of the valve body is reduced by 32.7%, the leakage rate is reduced to 0.008%, and the dynamic fatigue life is increased to 1.5 × 105 cycles under the commonly used engineering stress amplitude. The stress error between the simulation and the test is always less than 5%. The multi-objective optimization method under dynamic load in this paper can provide a theoretical basis for the reliable design and intelligent operation and maintenance of ultra-high pressure and ultra-wear-resistant pneumatic ball valves and promote their engineering applications in the fields of hydrogen energy storage and transportation and chemical industry.

The shift fork is a part of the automobile transmission, located at the lower end of the handle by flipping the intermediate transmission wheel so that the input/output speed ratio change is an essential structure in automobile transmission. In this paper, the variable shift fork is taken as the research object, and the finite element model of the shifting fork is established based on ABAQUS. The topology optimization of the shifting fork is carried out to meet the strength and stiffness requirements. The optimization model is analyzed according to the actual engineering conditions. The optimization aims to improve the strength and stiffness of the forks to reduce weight and improve performance. By comparing the mass of the optimized transmission fork before and after the optimization, compared with the original model of 1.20kg, the optimized transmission fork mass of 0.84kg is reduced by 0.35kg, and the weight reduction rate is 29.5%. It is indicated that the optimized transmission fork is lighter, stronger, and more efficient, which can improve the performance and economy of the vehicle. Pre-optimization and post-optimization scenarios were compared to determine the best solution. It can provide helpful information to car manufacturers and designers to optimize the design and performance of vehicle transmissions.

In order to have more accurate control over the compression molding of automobile coat rack, improve the quality of molding products, and achieve the goal of lightweight design, a novel mechanical model for the main two‐layer composite structure of the coat rack is proposed. In this regard, the main factors affecting the mechanical properties of the composite structure are obtained. The hot air convection is selected for the sheet preheating. During the experiment, the hot air temperature, preheating time, molding pressure, and pressing holding time are set to 250°C, 110 s, 13 MPa, and 80 s, respectively. Moreover, the error compensation method is applied to compensate for the shrinkage of the product during solidification and cooling. The LS‐DYNA finite element software is used to simulate the molding process of the main body of the coat rack, and the node force information with large deformation is obtained accordingly. The load mapping is used as the boundary condition of mold topology optimization, and the compression molding of the main body of the coat rack is optimized. A lightweight design process and method for the compression molding of automotive interior parts and a mathematical model for the optimization of the solid isotropic material penalty (SIMP) (power law) material interpolation of the concave and convex molds are established. Based on the variable density method, OptiStruct is used for the lightweight design of the convex and concave molds of the main body of the coat rack, which reduces the mold weight by 15.6% and meets the requirements of production quality and lightweight.

The first part of the paper is mainly historical, tracing the development of the motion picture art, particularly from the French poim of view. Various processes used for synchronizing sound and picture from about 1899 to the present are mentioned. Among these processes are those employing engravings on the film, and reliefs which act to vary the capacity in a high-frequency circuit. Reference is also made to magnetic wire processes and finally, the present-day method of recording sound photographically. Two variations of the latter process, viz., the fixed density method and the variable density method are explained. The discussion continues with various types of light valve recorders and sources of light. — The second part of the paper deals with the particular processes now employed in France, discussing particularly the various mechanical, electrical, optical, and acoustical processes which intervene between the studio and the review room. The matter of acoustics of the studio and the effect on the sound record is discussed at some length, as well as the effect of speed changes in the driving motor of the camera or recorder. Various other apparatus used in the studios are described.

Effects of the porous media distribution on the performance improvement for isothermal chamber