【正文】 : where [k] is the element stiffness matrix, [Be] is the derivative operator matrix, nhcuj7d3 is the displacements, and {re} is the element load vector which can be evaluated by: The use of a full threedimensional FEM analysis can achieve accurate warpage results, however, it is cumbersome when the shape of the part is very plicated. In this paper, a twodimensional FEM method, based on shell theory, was used because most injectionmolded parts have a sheetlike geometry in which the thickness is much smaller than the other dimensions of the part. Therefore, the part can be regarded as an assembly of flat elements to predict warpage. Each threenode shell element is a bination of a constant strain triangular element (CST) and a discrete Kirchhoff triangular element (DKT), as shown in Fig. 3. Thus, the warpage can be separated into planestretching deformation of the CST and platebending 13 deformation of the DKT, and correspondingly, the element stiffness matrix to describe warpage can also be divided into the stretchingstiffness matrix and bendingstiffness matrix. Fig. 3a–c. Deformation deposition of shell element in the local coordinate system. a Inplane stretching element b Platebending element c Shell element 3 Experimental validation To assess the usefulness of the proposed model and developed program, verification is important. The distortions obtained from the simulation model are pared to the ones from SL injection molding experiments whose data is presented in the literature [8]. A mon injection molded part with the dimensions of 36366 mm is considered in the experiment, as shown in Fig. 4. The thickness dimensions of the thin walls and rib are both mm。 1 附錄 2 Integrated simulation of the injection molding process with stereolithography molds Abstract Functional parts are needed for design veri?cation testing, ?eld trials, customer evaluation, and production planning. By eliminating multiple steps, the creation of the injection mold directly by a rapid prototyping (RP) process holds the best promise of reducing the time and cost needed to mold lowvolume quantities of parts. The potential of this integration of injection molding with RP has been demonstrated many times. What is missing is the fundamental understanding of how the modi?cations to the mold material and RP manufacturing process impact both the mold design and the injection molding process. In addition, numerical simulation techniques have now bee helpful tools of mold designers and process engi neers for traditional injection molding. But all current simulation packages for conventional injection molding are no longer applicable to this new type of injection molds, mainly because the property of the mold material changes greatly. In this paper, an integrated approach to acplish a numerical simulation of injection molding into rapidprototyped molds is established and a corresponding simulation system is developed. Comparisons with experimental results are employed for veri?cation, which show that the present scheme is well suited to handle RP fabricated stereolithography (SL) molds. Keywords Injection molding Numerical simulation Rapid prototyping 1 Introduction In injection molding, the polymer melt at high temperature is injected into the mold under high pressure [1]. Thus, the mold material needs to have thermal and mechanical properties capable of withstanding the temperatures and pressures of the molding cycle. The focus of many studies has been to create the injection mold directly by a rapid prototyping (RP) process. By eliminating multiple steps, this method of tooling holds the best promise of reducing the time and cost needed to create lowvolume quantities of parts in a production material. The potential of integrating injection molding with RP technologies has been demonstrated many times. The properties of RP molds are very different from those of traditional metal molds. The key differ ences are the properties of thermal conductivity and elastic modulus (rigidity). For example, the polymers used in RPfabricated stereolithography (SL) molds have a thermal conductivity that is less than one 2 thousandth that of an aluminum tool. In using RP technologies to create molds, the entire mold design and injectionmolding process parameters need to be modi?ed and optimized from traditional methodologies due to the pletely different tool material. However, there is still not a fundamental understanding of how the modi?cations to the mold tooling method and material impact both the mold design and the injection molding process parameters. One cannot obtain reasonable results by simply changing a few material properties in current models. Also, using traditional approaches when making actual parts may be generating suboptimal results. So there is a dire need to study the interaction between the rapid tooling (RT) process and material and injection molding, so as to establish the mold design criteria and techniques for an RToriented injection molding process. In addition, puter simulation is an effective approach for predicting the quality of molded parts. Commercially available simulation packages of the traditional injection molding process have now bee routine tools of the mold designer and process engineer [2]. Unfortunately, current simulation programs for conventional injection molding are no longer applicable to RP molds, because of the dramatically dissimilar tool material. For instance, in using the existing simulation software with aluminum and SL molds and paring with experimental results, though the simulation values of part distortion are reasonable for the aluminum mold, results are unacceptable, with the error exceeding 50%. The distortion during injection molding is due to shrinkage and warpage of the plastic