Geometry.The geometry of the element is defined by the placement of the nodal points.Most elements used in practice have fairly simple geometries.In one-dimension,elements are usually straight lines or curved segments. In two dimensions they are of triangular or quadrilateral shape.In three dimensions the most common shapes are tetrahedra,pentahedra(also called wedges or prisms),and hexahedra(also called cuboids or"bricks"). Degrees of freedom.The degrees of freedom(DOF)specify the state of the element.They also function as "handles"through which adjacent elements are connected.DOFs are defined as the values (and possibly derivatives)of a primary field variable at nodal points.The actual selection depends on criteria studied at length in Part ll.Here we simply note that the key factor is the way in which the primary variable appears in the mathematical model.For mechanical elements,the primary variable is the displacement field and the DOF for many(but not all)elements are the displacement components at the nodes. Nodal forces.There is always a set of nodal forces in a one-to-one correspondence with degrees of freedom.In mechanical elements the correspondence is established through energy arguments. Constitutive properties.For a mechanical element these are relations that specify the material behavior.For example,in a linear elastic bar element it is sufficient to specify the elastic modulus E and the thermal coefficient of expansion a. Fabrication properties.For mechanical elements these are fabrication properties which have been integrated out from the element dimensionality.Examples are cross sectional properties of MoM elements such as bars,beams and shafts,as well as the thickness of a plate or shell element.Geometry. The geometry of the element is defined by the placement of the nodal points. Most elements used in practice have fairly simple geometries. In one-dimension, elements are usually straight lines or curved segments. In two dimensions they are of triangular or quadrilateral shape. In three dimensions the most common shapes are tetrahedra, pentahedra (also called wedges or prisms), and hexahedra (also called cuboids or “bricks”). Degrees of freedom. The degrees of freedom (DOF) specify the state of the element. They also function as “handles” through which adjacent elements are connected. DOFs are defined as the values (and possibly derivatives) of a primary field variable at nodal points. The actual selection depends on criteria studied at length in Part II. Here we simply note that the key factor is the way in which the primary variable appears in the mathematical model. For mechanical elements, the primary variable is the displacement field and the DOF for many (but not all) elements are the displacement components at the nodes. Nodal forces. There is always a set of nodal forces in a one-to-one correspondence with degrees of freedom. In mechanical elements the correspondence is established through energy arguments. Constitutive properties. For a mechanical element these are relations that specify the material behavior. For example, in a linear elastic bar element it is sufficient to specify the elastic modulus E and the thermal coefficient of expansion α. Fabrication properties. For mechanical elements these are fabrication properties which have been integrated out from the element dimensionality. Examples are cross sectional properties of MoM elements such as bars, beams and shafts, as well as the thickness of a plate or shell element