It's recommended that the term coupled in temperature and strain is nonlinear and is significant in thermoelastic theory. Using the solution of linear coupled and uncoupled theory and selecting appropriate general coordinates, authers approach the nonlinear coupled problems with a variational method. A solution to the problem in half space, is given. It is shown that the difference between the nonlinear coupled theory and the linear coupled or uncoupled theory would be notable when the amplitute of temperature is much larger than that of the reference slate.