How to use wp_nav_menu to create custom dropdown menu?

Use wp_nav_menu() with proper parameters to add the dropdown-menu forAnimate class, to remove the wrapper and to add the role attribute:

<ul class="nav navbar-nav">
    <li class="active"><a href="https://wordpress.stackexchange.com/questions/255497/index.html">Home</a></li>
    <li><a href="category.html">Category Page</a></li>
    <li><a href="article.html">Article Page</a></li>
    <li class="dropdown">
        <a href="#" class="dropdown-toggle" data-toggle="dropdown"> Category Type A <span class="caret"></span></a>
        <?php wp_nav_menu(array(
            'menu'       => 'my_menu_name', // specify the menu name
            'menu_class' => 'dropdown-menu forAnimate', // add classes for the dropdown
            'container'  => '', // don't wrap the menu in <div>
            'items_wrap' => '<ul id="%1$s" class="%2$s" role="menu" >%3$s</ul>',
        ));?>
    </li>
</ul>

'<ul id="%1$s" class="%2$s" role="menu" >%3$s</ul>' part is intended to keep id and class as is and to add the role attribute.

Not tested, though.

See wp_nav_menu() for more information.