The penalty and Lagrange method are the most well known methods in incompressible material solutions. In the Lagrange method, incompressibility constraint is imposed on each element. To obtain acceptable results from this method, some conditions, i.e. Babuska and Brezzi conditions, should be satisfied. These conditions may not be satisfied for all problems. Specially, if this method is used for triangular elements in some cases it may yield unreliable results; this effect is named “ Volumetric locking “. So this method loses its generality. In penalty method the incompressible constraint is imposed , the incompressible problems. In present research a new iteractive method based on Logrange multipliers method is proposed for quadrilateral and triangular elements . In each iteration, the forces that cause volumetric changes are eliminated from whole system. Consequently after few numbers of iterations, the final domain will have no volumetric modes in displacement field. For imposing incompressibility constraint on triangular elements, an extra node is defined at the center of element and consequently each triangular element is divided into three incompressibility constraint is not imposed directly to triangular elements. Because the incompressibility constraint is not imposed directly to triangular elements, the method does not show volumetric locking. Some examples are presented and the results are compared with available solution in literature.
