Research On Theory And Application Of Topology Optimization Of Truss Structures

Truss structures have advantages of light weight?low cost?simple construction and so on,and have been widely used in fields of engineering,such as engineering machinery?bridge design?construction support?building structures?water conservency flume?gate support?transmission network and other aspects,playing an increasingly important role in constructions?To illustrate the space camera as an example,the structures between the primary and second mirror of large and medium-sized space optical cameras in foreign are mostly trusses?The design idea is based on the principle of structural optimization that the bending load of variable compent is tensible or compressive,which has advantages of high specific stiffness?light weight and suitability for the layout of long focal length optical system?In addition,truss structures are also used in aircraft?satellite?space station and other aerospace structures,having a wide range of applications?The traditional way of obtaining the optimal truss layout is based on the approximate truss-like results obtained via the continuum topology optimization,but it has some defects,such as the uncertainty of equivalence and the unknown size?In contrast,these problems can be avoided by truss topology optimization?Therefore,we try to seek an effective approach to apply the truss topology optimization method to practical engineering problems?On this foundation,key components of the photoelectric theodolite are designed by trusses,that is,truss structures are used to replace the original continuum structures?The aim is to provide a lightweight design scheme,which will make the weight of the whole structure is the mimimum without sacrificing other performances?For this reason,the dissertation mainly contains the following contexts:Research on generating the truss ground structure for design areas in arbitrary shape:In light of characteristics of engineering problems with complex and irregular geometry,we expand and improve the method of generating the gound structure based on the finite element mesh?Using the collision detection technique,together with idea of discrete approximation,construction of the ground structure in part/full connections for complex design domains containing any number of concave zones is successfully implemented.At the same time,fast and efficient searching of overlapping members is achieved based on the difference of node coordinates?Research on the rationality of the construction of the ground structure:According to the force transmission path method,we propose a method to generate the gound structure based on the principle stress trajectories of the design domain under the boundary condition,that is,the intersections of these trajectories are treated as the nodes of bars to construct member connections,which will include good candidate bars?The ground structure obtained can result in a good numerical solution,which is close to the optimal solution,with fewer nodes and members when compared to the traditional ways?Morever,by combining the superposition principle of component loads,this method is successfully extended to multiple cases?Research on the method of solving large-scale truss topology optimization problems efficiently and quickly:In view of the huge number of full connections in ground structure and long time of calculation,we modify and improve the traditional members-adding method?By adopting the members-adding order that "from short to long" and limit the number of bars added in each step properly,the scale of members in LP is decreased significantly,as well as the computation time?In addition,by combining with the principle stress trajectories and the reasonable stopping criterion,the phenomenon "ersatz virtual displacements" in traditional members-adding methods is effectively alleviated,and the efficiency of solving large-scale truss topology optimization in plastic design is improved largely?Research on truss topology optimization in elastic design:Starting from the semidefiniting programming,we derive the equivalent SDP models with two popular problems in elastic design:The problem miminizes the volume of the structure,restricted to compliance;and the problem miminizes the compliance of the structure,restricted to volume?The numerical and theorical results show that the consistency of topology structures of these two models?Besides,the difference and similarity of topology results between truss elastic design and plastic design in single load condition and multiple load conditions are shown by numerical examples as well?Research on the lightweight design scheme of key components of the photoelectric theodolite:We analyze the connection between the turntable and four-way structure,and establish the reasonable finite element model,together with the truss ground structure?The truss topology optimization in elastic design and plastic design are carried out,respectively?As a supplement,the continuum topology optimization is also carried out?The lightweight design scheme is determined after comparing all potential optimization results,then the finite element analysis of the modified structure is conducted?The result shows that the lightweight design scheme can improve the weight of the structure and meet the initial design expectations while satisfying the indexes?...