How do I format date value as yyyy-mm-dd using SSIS expression builder?

Correct expression is

"source " + (DT_STR,4,1252)DATEPART( "yyyy" , getdate() ) + "-" +
RIGHT("0" + (DT_STR,4,1252)DATEPART( "mm" , getdate() ), 2) + "-" +
RIGHT("0" + (DT_STR,4,1252)DATEPART( "dd" , getdate() ), 2) +".CSV"

Looks like you created a separate question. I was answering your other question How to change flat file source using foreach loop container in an SSIS package? with the same answer. Anyway, here it is again.

Create two string data type variables namely DirPath and FilePath. Set the value C:\backup\ to the variable DirPath. Do not set any value to the variable FilePath.

Select the variable FilePath and select F4 to view the properties. Set the EvaluateAsExpression property to True and set the Expression property as @[User::DirPath] + "Source" + (DT_STR, 4, 1252) DATEPART("yy" , GETDATE()) + "-" + RIGHT("0" + (DT_STR, 2, 1252) DATEPART("mm" , GETDATE()), 2) + "-" + RIGHT("0" + (DT_STR, 2, 1252) DATEPART("dd" , GETDATE()), 2)