To evaluate the thermal deformation induced by 3D Printing (Three Dimensional Printing) process, a novel meshless analysis procedure is established. To account for the heat transfer and solidification effects of each printing layer from liquid to solid phase transition, the layer temperature is measured by the implanted thermocouples. Based on the temperature variation measured, the printing layer temperature can be averaged and considered as uniform for thermal analysis. In addition, as observed by the deformation of the printed target through experiment, only linear thermal elastic analysis is performed.

A rigorous algorithm for simulating the 3D Printing process is presented herein. Since the interpolation functions are no longer polynomials, a simple integration scheme using uniform integration points is applied to calculate the global stiffness matrix. Thus, the density and location of the integration points can be easily adjusted to fulfill the required accuracy. Further, for practical implementation, the simulation is also carried out by the concept of equivalent layer.

Demonstrative cases of printing a rectangular PLA (Polylactic Acid) brick are tackled to prove the accuracy and efficiency of the proposed meshless analysis procedure. The effects of layer thickness, equivalent layer and slenderness ratio on the thermal deformation of the printed brick are also investigated.

为了评估3D打印（三维打印）过程引起的热变形，建立了一种新颖的无网格分析程序。为了说明每个印刷层从液相到固相转变的传热和固化效果，通过注入的热电偶测量层温度。基于测得的温度变化，可以对印刷层温度进行平均，并认为对于热分析而言是均匀的。另外，如通过实验打印的目标的变形所观察到的，仅执行线性热弹性分析。

本文介绍了一种用于模拟3D打印过程的严格算法。由于插值函数不再是多项式，因此使用使用统一积分点的简单积分方案来计算全局刚度矩阵。因此，可以容易地调整积分点的密度和位置，以满足所需的精度。此外，对于实际实现，还通过等效层的概念来进行仿真。

解决了印刷矩形PLA（聚乳酸）砖的演示案例，以证明所提出的无网格分析程序的准确性和效率。还研究了层厚，当量层和长细比对印刷砖热变形的影响。