| As a new type of ultra-lightweight material,the multi-material lattice structure is widely used in various fields due to its high specific stiffness,high specific strength and designability of material properties.However,due to its complex microstructure,it is difficult to analyze using traditional finite element method,and its design optimization is even more difficult.Based on the asymptotic homogenization method,this thesis obtains the equivalent performance of the lattice structure,and explores the influence of different geometric factors on the equivalent performance of the lattice structure.The lattice structure is regarded as an equivalent material.Subsequently,topology optimization is used to optimize the spatial distribution of lattice materials.In order to reduce the thermal stress of the structure under the combined action of thermal load and mechanical load,the global maximum thermal stress is used as the objective function,and the compliance is used as the constraint,and the macromicro integrated optimization design of the lattice filling structure is realized.The commercial software was re-developed to realize the parametric modeling of the lattice filling structure.In order to broaden the application range of lattice materials,a lattice filling method for complex parts is proposed,and the lattice structure is applied to complex parts.And on this basis,for the high and low temperature heterogeneous connection structure,a lattice filling method that matches the thermal expansion of the connected part is proposed to reduce the thermal stress of the connected part.Finally,the design idea of matching thermal expansion is introduced into the optimization design of lattice filling structure to realize the macro and micro integrated design of matching thermal expansion lattice filling structure.The main work of this article includes:1)Based on the bi-material pyramid structure,we study the mechanism and design scope of the designable thermal expansion of the structure.An orthotropic lattice structure with a designable thermal expansion coefficient is formed.The simulation analysis method is used to create a lattice discrete structure and a homogenized solid structure to verify the accuracy of the asymptotic homogenization method in predicting the equivalent properties of materials under different unit cell numbers,load conditions and geometric shapes.We calculate the equivalent performance of the lattice structure,explore the influence of different geometric factors on the equivalent properties of the lattice structure,and construct the interpolated relationship between the structure’s equivalent properties and the amount of material.2)Taking the minimization of the maximum thermal stress of the structure as the objective function,and the compliance and volume as the constraint,we construct an optimization model of the minimum structural thermal stress under the combined action of mechanical and thermal loads.We derive the expression and sensitivity of stress,thermal stress and maximum thermal stress,and verify the correctness of the sensitivity by the difference method.Numerical examples are used to verify the effectiveness of the optimization model.Finally,by combining the lattice structure interpolation relationship and topology optimization,the macro and micro integrated design method of the lattice structure is realized.3)Based on the macro operation of the commercial software,the secondary development is carried out to realize the parametric modeling of the lattice structure.A design method of lattice filling to ensure the integrity of the lattice structure is proposed to realize the lattice filling and three-dimensional modeling of complex parts.Aiming at the heterogeneous connection structure with high and low temperature,a lattice filling method is proposed that matches the thermal stress of the connected part.Through the simulation verification of the filling result,this method can actually reduce the thermal stress of the connected part.4)The design idea of matching thermal expansion coefficient is introduced in the optimization process.By comparing the optimized design of matching thermal expansion lattice structure and the optimized design of zero expansion lattice structure,the effectiveness based on matching thermal expansion coefficient is verified in reducing structural thermal stress. |
